A261731 Initial member of five twin prime pairs with gap 210 between them.
1308497, 3042491, 3042701, 7445309, 20031101, 31572521, 44687987, 54266291, 141208619, 182316521, 237416369, 357080021, 448436321, 611641187, 699458411, 761126027, 774997367, 794065967, 836452961, 915215591, 944958941, 1009194617, 1581935939, 1763255561, 1871007371
Offset: 1
Keywords
Examples
1308497 appears in this sequence because: (a) {1308497, 1308499}, {1308707, 1308709}, {1308917, 1308919}, {1309127, 1309129}, and {1309337, 1309339} are five twin prime pairs; (b) the gap between each twin prime pair {1308707 - 1308497} = {1308917-1308707} = {1309127 - 1308917} = {1309337 - 1309127} = 210.
Links
- K. D. Bajpai and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 46 terms from K. D. Bajpai]
Programs
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Magma
[p: p in PrimesUpTo (100000) | IsPrime(p+2) and IsPrime(p+210) and IsPrime(p+212) and IsPrime(p+420) and IsPrime(p+422) and IsPrime(p+630) and IsPrime(p+632) and IsPrime(p+840) and IsPrime(p+842) ];
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Maple
select(p -> andmap(isprime, [p, p+2, p+210, p+212, p+420, p+422, p+630, p+632, p+840, p+842]),[seq(p, p=1..2*10^7)]);
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Mathematica
k = 210; Select[Prime@Range[6*10^7], PrimeQ[# + 2] && PrimeQ[# + k] && PrimeQ[# + k + 2] && PrimeQ[# + 2 k] && PrimeQ[# + 2 k + 2] && PrimeQ[# + 3 k] && PrimeQ[# + 3 k + 2] && PrimeQ[# + 4 k] && PrimeQ[# + 4 k + 2] &] Select[Prime[Range[93*10^6]],AllTrue[#+{2,210,212,420,422,630,632,840,842},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 05 2018 *) -
PARI
forprime(p= 1,3*10^9, if(isprime(p+2) && isprime(p+210) && isprime(p+212) && isprime(p+420) && isprime(p+422) && isprime(p+630) && isprime(p+632) && isprime(p+840) && isprime(p+842), print1(p,", ")));
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Perl
use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 2, 210, 212, 420, 422, 630, 632, 840, 842); # Dana Jacobsen, Oct 02 2015
Comments