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
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Aug 30 2015
STATUS
approved