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Search: a128342 -id:a128342
Displaying 1-10 of 23 results found. page 1 2 3
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A128336 Numbers k such that (6^k + 5^k)/11 is prime. +10
26
3, 5, 17, 397, 409, 643, 1783, 2617, 4583, 8783 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
No other terms less than 100000. - Robert Price, May 11 2012
LINKS
Table of n, a(n) for n=1..10.
MATHEMATICA
k=6; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
PROG
(PARI) forprime(p=3, 1e4, if(ispseudoprime((6^p+5^p)/11), print1(p", "))) \\ Charles R Greathouse IV, Jul 16 2011
CROSSREFS
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.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
a(7)-a(9) from Alexander Adamchuk, May 04 2010
One more term (8783) added (unknown discoverer) corresponding to a probable prime with 6834 digits by Jean-Louis Charton, Oct 06 2010
STATUS
approved
A128347 Numbers k such that (11^k - 5^k)/6 is prime. +10
26
5, 41, 149, 229, 263, 739, 3457, 20269, 98221 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(10) > 10^5. - Robert Price, Jan 24 2013
LINKS
Table of n, a(n) for n=1..9.
MATHEMATICA
k=11; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
PROG
(PARI) is(n)=isprime((11^n-5^n)/6) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
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.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
a(7)-a(9) from Robert Price, Jan 24 2013
STATUS
approved
A128341 Numbers k such that (12^k + 5^k)/17 is prime. +10
22
3, 5, 13, 347, 977, 1091, 4861, 4967, 34679 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(10) > 10^5. - Robert Price, May 05 2013
LINKS
Table of n, a(n) for n=1..9.
MATHEMATICA
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 *)
PROG
(PARI) is(n)=isprime((12^n+5^n)/17) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128342, A128343.
Cf. A004061, A082182, A121877, A059802.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
Two more terms (a(7) and a(8)) from Harvey P. Dale, Jul 24 2012
a(9) from Robert Price, May 05 2013
STATUS
approved
A128344 Numbers k such that (7^k - 5^k)/2 is prime. +10
22
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)
OFFSET
1,1
COMMENTS
All terms are primes.
No other terms less than 10^5. - Robert Price, May 28 2012
No other terms less than 10^6. - Jon Grantham, Jul 29 2023
LINKS
Table of n, a(n) for n=1..17.
Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.
MATHEMATICA
k=7; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
PROG
(PARI) is(n)=isprime((7^n-5^n)/2) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
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.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
a(7)-a(9) from Robert Price, May 28 2012
a(10)-a(17) from Jon Grantham, Jul 29 2023
STATUS
approved
A128339 Numbers k such that (9^k + 5^k)/14 is prime. +10
21
3, 5, 13, 17, 43, 127, 229, 277, 6043, 11131, 11821 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(12) > 10^5. - Robert Price, Dec 26 2012
LINKS
Table of n, a(n) for n=1..11.
MATHEMATICA
k=9; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
PROG
(PARI) is(n)=isprime((9^n+5^n)/14) \\ Charles R Greathouse IV, Feb 17 2017
(Magma) [n: n in [3..300] |IsPrime((9^n + 5^n) div 14)]; // Vincenzo Librandi, Nov 02 2018
CROSSREFS
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.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
3 more PRP terms from Sean A. Irvine, Oct 01 2009
STATUS
approved
A128340 Numbers k such that (11^k + 5^k)/16 is prime. +10
20
7, 11, 181, 421, 2297, 2797, 4129, 4139, 7151, 29033 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(11) > 10^5. - Robert Price, Feb 09 2013
LINKS
Table of n, a(n) for n=1..10.
MATHEMATICA
k=11; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
PROG
(PARI) is(n)=isprime((11^n+5^n)/16) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128341, A128342, A128343.
Cf. A004061, A082182, A121877, A059802.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
a(5)-a(10) from Robert Price, Feb 09 2013
STATUS
approved
A128346 Numbers k such that (9^k - 5^k)/4 is prime. +10
20
3, 11, 17, 173, 839, 971, 40867, 45821, 147503 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(9) > 10^5. - Robert Price, Jan 19 2013
a(10) > 10^6. - Jon Grantham, Jul 29 2023
LINKS
Table of n, a(n) for n=1..9.
Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.
MATHEMATICA
k=9; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
PROG
(PARI) is(n)=isprime((9^n-5^n)/4) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A062572, A128344, A128345, 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.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
a(7)-a(8) from Robert Price, Jan 19 2013
a(8) corrected by Robert Price, Jan 20 2013
a(9) from Jon Grantham, Jul 29 2023
STATUS
approved
A128348 Numbers k such that (12^k - 5^k)/7 is prime. +10
20
2, 3, 31, 41, 53, 101, 421, 1259, 4721, 45259 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
a(11) > 10^5. - Robert Price, Mar 02 2013
LINKS
Table of n, a(n) for n=1..10.
MATHEMATICA
k=12; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
PROG
(PARI) is(n)=isprime((12^n-5^n)/7) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A062572, A128344, A128345, A128346, A128347, A128349, A128350, A128351, A128352, A128353, A128354.
Cf. A004061, A082182, A121877, A059802.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
a(8) and a(9) from Ray G. Opao, Jul 01 2012
a(10) from Robert Price, Mar 02 2013
STATUS
approved
A128337 Numbers k such that (7^k + 5^k)/12 is prime. +10
19
11, 31, 173, 271, 547, 1823, 2111, 5519, 7793, 22963, 41077, 49739 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
a(13) > 10^5. - Robert Price, Nov 20 2012
LINKS
Table of n, a(n) for n=1..12.
MATHEMATICA
k=7; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n, 1, 100}]
PROG
(PARI) is(n)=isprime((7^n+5^n)/12) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A057171, A082387, A122853, A128335, A128336, A128338, A128339, A128340, A128341, A128342, A128343.
Cf. A004061, A082182, A121877, A059802.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
a(6)-a(12) from Robert Price, Nov 20 2012
STATUS
approved
A128345 Numbers k such that (8^k - 5^k)/3 is prime. +10
19
2, 19, 1021, 5077, 34031, 46099, 65707, 347437 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All terms are primes.
No further terms up to 5000 - Harvey P. Dale, Mar 23 2011
a(8) > 10^5 - Robert Price, Dec 22 2012
a(9) > 10^6 - Jon Grantham, Jul 29 2023
LINKS
Table of n, a(n) for n=1..8.
Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.
MATHEMATICA
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 *)
PROG
(PARI) is(n)=isprime((8^n-5^n)/3) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
Cf. A062572, A128344, 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.
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 27 2007
EXTENSIONS
a(4)-a(7) from Robert Price, Dec 22 2012
a(8) from Jon Grantham, Jul 29 2023
STATUS
approved
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Last modified August 30 07:09 EDT 2024. Contains 375532 sequences. (Running on oeis4.)