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

1,1

Comments

More precisely, primes p such that p+2, p+210, p+212, p+420, p+422, p+630, p+632, p+840, p+842 are all primes.

All the terms in this sequence are congruent to 2 (mod 3).

Links

K. D. Bajpai and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 46 terms from K. D. Bajpai]

Example

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.

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)]);

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 *)

Prog

(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, ", ")));
(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) ];
(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

Crossrefs

Cf. A077800, A113274, A253624, A261701.

Sequence in context: A253799 A186138 A066702 * A141592 A234710 A116495

Adjacent sequences: A261728 A261729 A261730 * A261732 A261733 A261734

Keyword

nonn

Author

K. D. Bajpai, Aug 30 2015

Status

approved