Search: a128342 -id:a128342
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A128336
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Numbers k such that (6^k + 5^k)/11 is prime.
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+10
26
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
No other terms less than 100000. - Robert Price, May 11 2012
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LINKS
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MATHEMATICA
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k=6; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
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PROG
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CROSSREFS
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Cf. A057171, A082387, A122853, A128335, A128337, A128338, A128339, A128340, A128341, A128342, A128343, A004061, A082182, A121877, A059802, A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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One more term (8783) added (unknown discoverer) corresponding to a probable prime with 6834 digits by Jean-Louis Charton, Oct 06 2010
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STATUS
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approved
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A128347
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Numbers k such that (11^k - 5^k)/6 is prime.
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+10
26
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
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LINKS
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MATHEMATICA
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k=11; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
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PROG
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CROSSREFS
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Cf. A062572, A128344, A128345, A128346, A128348, A128349, A128350, A128351, A128352, A128353, A128354. Cf. A004061, A082182, A121877, A059802. Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A128341
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Numbers k such that (12^k + 5^k)/17 is prime.
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+10
22
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
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LINKS
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MATHEMATICA
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k=12; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
Select[Range[1100], PrimeQ[(12^#+5^#)/17]&] (* Harvey P. Dale, Jul 24 2012 *)
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PROG
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CROSSREFS
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Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128342, A128343.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A128344
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Numbers k such that (7^k - 5^k)/2 is prime.
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+10
22
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3, 5, 7, 113, 397, 577, 7573, 14561, 58543, 100019, 123407, 136559, 208283, 210761, 457871, 608347, 636043
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
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LINKS
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MATHEMATICA
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k=7; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
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PROG
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CROSSREFS
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Cf. A062572, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354. Cf. A004061, A082182, A121877, A059802. Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A128339
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Numbers k such that (9^k + 5^k)/14 is prime.
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+10
21
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3, 5, 13, 17, 43, 127, 229, 277, 6043, 11131, 11821
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
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LINKS
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MATHEMATICA
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k=9; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
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PROG
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(Magma) [n: n in [3..300] |IsPrime((9^n + 5^n) div 14)]; // Vincenzo Librandi, Nov 02 2018
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CROSSREFS
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Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128340, A128341, A128342, A128343. Cf. A004061, A082182, A121877, A059802. Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A128340
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Numbers k such that (11^k + 5^k)/16 is prime.
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+10
20
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
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LINKS
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MATHEMATICA
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k=11; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
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PROG
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CROSSREFS
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Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128341, A128342, A128343.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A128346
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Numbers k such that (9^k - 5^k)/4 is prime.
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+10
20
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
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LINKS
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MATHEMATICA
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k=9; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
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PROG
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CROSSREFS
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Cf. A062572, A128344, A128345, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A128348
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Numbers k such that (12^k - 5^k)/7 is prime.
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+10
20
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
Primality of the primes formed by a(8) and a(9) were certified by Primo. - Ray G. Opao, Jul 01 2012
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LINKS
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MATHEMATICA
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k=12; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
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PROG
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CROSSREFS
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Cf. A062572, A128344, A128345, A128346, A128347, A128349, A128350, A128351, A128352, A128353, A128354.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A128337
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Numbers k such that (7^k + 5^k)/12 is prime.
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+10
19
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11, 31, 173, 271, 547, 1823, 2111, 5519, 7793, 22963, 41077, 49739
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
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LINKS
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MATHEMATICA
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k=7; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
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PROG
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CROSSREFS
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Cf. A057171, A082387, A122853, A128335, A128336, A128338, A128339, A128340, A128341, A128342, A128343.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A128345
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Numbers k such that (8^k - 5^k)/3 is prime.
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+10
19
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OFFSET
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1,1
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COMMENTS
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All terms are primes.
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LINKS
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MATHEMATICA
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k=8; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 200}]
Select[Range[5000], PrimeQ[(8^#-5^#)/3]&] (* Harvey P. Dale, Mar 23 2011 *)
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PROG
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CROSSREFS
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Cf. A062572, A128344, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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