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A261731 Initial member of five twin prime pairs with gap 210 between them. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 18:56 EDT 2021. Contains 347608 sequences. (Running on oeis4.)