OFFSET
1,1
COMMENTS
More precisely, primes p such that p + 2, p + 210, p + 212, p + 420, p + 422, p + 630, p + 632 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 865 terms from K. D. Bajpai]
Luis Rodriguez and Carlos Rivera, Gaps between consecutive twin pairs, The Prime Puzzles and Problems Connection.
EXAMPLE
599 appears in the sequence because: (a) {599,601}, {809, 811}, {1019, 1021}, {1229, 1231} are four (not consecutive) twin prime pairs; (b) the gap between each twin prime pair (809 - 599) = (1019 - 809) = (1229 - 1019) = 210.
MAPLE
select(p -> andmap(isprime, [p, p+2, p+210, p+212, p+420, p+422, p+630, p+632]), [seq(p, p=1..10^5)]);
MATHEMATICA
k = 210; Select[Prime@Range[10^7], PrimeQ[# + 2] && PrimeQ[# + k] && PrimeQ[# + k + 2] && PrimeQ[# + 2 k] && PrimeQ[# + 2 k + 2] && PrimeQ[# + 3 k] && PrimeQ[# + 3 k + 2] &]
Select[Prime[Range[400000]], AllTrue[#+{2, 210, 212, 420, 422, 630, 632}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 17 2019 *)
PROG
(PARI) forprime(p= 1, 100000, if(isprime(p+2) && isprime(p+210) && isprime(p+212) && isprime(p+420) && isprime(p+422) && isprime(p+630) && isprime(p+632), 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) ];
(Perl) use ntheory ":all"; say join ", ", grep { is_prime($_+210) && is_prime($_+212) && is_prime($_+420) && is_prime($_+422) && is_prime($_+630) && is_prime($_+632) } @{twin_primes(1e8)}; # Dana Jacobsen, Sep 02 2015
(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e8, 2, 210, 212, 420, 422, 630, 632); # Dana Jacobsen, Oct 03 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Aug 28 2015
STATUS
approved