Search: a103523 -id:a103523
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A103534
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Concatenations of pairs of primes that differ by 1000.
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+10
3
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131013, 191019, 311031, 611061, 971097, 1031103, 1091109, 1511151, 1631163, 1811181, 1931193, 2231223, 2291229, 2771277, 2831283, 3071307, 3671367, 3731373, 4091409, 4331433, 4391439, 4871487, 4991499, 5231523, 5711571
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OFFSET
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1,1
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COMMENTS
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All terms are multiples of 3.
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LINKS
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FORMULA
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a(n) = Concatenate(P, P+1000) iff P prime and P+1000 prime.
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EXAMPLE
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1811181 is in this sequence because 181 is prime, 181+1000 = 1181 is prime and those two primes are concatenated.
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MATHEMATICA
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10001#+1000&/@Select[Prime[Range[150]], PrimeQ[#+1000]&] (* Harvey P. Dale, Sep 01 2017 *)
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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A103576
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Concatenations of pairs of primes that differ by 1000000.
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+10
2
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31000003, 371000037, 1511000151, 1931000193, 1991000199, 2111000211, 3131000313, 3671000367, 3971000397, 4091000409, 4571000457, 5411000541, 5471000547, 5771000577, 6191000619, 6911000691, 8291000829, 8591000859
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OFFSET
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1,1
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COMMENTS
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After the first element, 31000003, which is prime, integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for 3671000367 = 3 x 1223666789, 4571000457 = 3 x 1523666819, 5411000541 = 3 x 1803666847, 9071000907 = 3 x 3023666969.
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LINKS
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FORMULA
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a(n) = Concatenate(P, P+1000000) iff P prime and P+1000000 prime.
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EXAMPLE
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Prime(47) = 211 and 211 + 1000000 = Prime(78515) = 1000211. Concatenating these two primes gives 2111000211 = 3^4 * 17^2 * 31 * 2909.
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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A103617
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Concatenations of pairs of primes that differ by 10^9.
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+10
2
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71000000007, 971000000097, 1031000000103, 1811000000181, 2231000000223, 2411000000241, 2711000000271, 3491000000349, 4091000000409, 4331000000433, 4391000000439, 6071000000607, 6131000000613, 7871000000787, 8291000000829
(list;
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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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Integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for Prime(42) concatenated with Prime(50847544) = 1811000000181 = 3 x 603666666727.
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LINKS
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FORMULA
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a(n) = Concatenate(P, P+1000000000) iff P prime and P+1000000000 prime.
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EXAMPLE
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181 is prime, 181+10^9 = 1000000181 is prime, so their concatenation is an element of this sequence: 1811000000181. Coincidentally, prime(181)+10^9 = 1000001087 is also prime.
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MATHEMATICA
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FromDigits[Join[IntegerDigits[#], IntegerDigits[#+10^9]]]&/@Select[Prime[ Range[ 200]], PrimeQ[ #+ 10^9]&] (* Harvey P. Dale, May 14 2022 *)
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CROSSREFS
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Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719, A103523, A103534, A103576.
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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A104873
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Concatenations of pairs of primes that differ by 10^12.
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+10
1
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611000000000061, 1631000000000163, 1931000000000193, 2111000000000211, 2711000000000271, 3311000000000331, 5471000000000547, 6611000000000661, 7511000000000751, 7871000000000787, 9971000000000997, 10511000000001051
(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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Integers in this sequence can never be prime, as they are all multiples of 3. They can be semiprimes, as is the case for Prime(177) concatenated with Prime(37607912056) = 10511000000001051 = 3 * 3503666666667017.
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LINKS
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FORMULA
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a(n) = Concatenate(P, P+10^12) iff P prime and P+10^12 prime.
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EXAMPLE
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61 is prime, specifically prime(18) and 61 + 10^12 is prime, specifically prime(7607912020), so their concatenation is in this sequence: 611000000000061. The concatenation is not itself prime, as it equals 3 * 7 * 23 * 1265010351967.
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MATHEMATICA
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#*10^13+10^12+#&/@Select[Prime[Range[200]], PrimeQ[#+10^12]&] (* Harvey P. Dale, Jan 18 2021 *)
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CROSSREFS
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Cf. A000040, A001358, A023201, A100750, A103195, A103206, A104718, A104719, A103523, A103534, A103576, A103617.
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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