A262176 Numbers n where n-17, n-1, n+1 and n+17 are consecutive primes.

3390, 66570, 70140, 84810, 132330, 136710, 222840, 225750, 242730, 271770, 288930, 320010, 330330, 377370, 390390, 414330, 463890, 489960, 505710, 644670, 758340, 819390, 830310, 857010, 895650, 906540, 908910, 924810, 952380, 968520, 974820

Offset

1,1

Comments

This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Primes

Example

3390 is the average of the four consecutive primes 3373, 3389, 3391, 3407.
66570 is the average of the four consecutive primes 66553, 66569, 66571, 66587.

Mathematica

Select[Prime@ Range@ 50000, NextPrime[#, {1, 2, 3}] == {16, 18, 34} + # &] + 17 (* Giovanni Resta, Sep 14 2015 *)

Prog

(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 3000001, 6):
..if isprime(i-1) and isprime(i+1) and prevprime(i-1)==i-17 and nextprime(i+1)==i+17 : print (i, end=', ')
(PARI) list(l)=for(i=1, l, p=prime(i); if(p+16==prime(i+1)&&p+18==prime(i+2)&&p+34==prime(i+3), print1(p+17, ", "))) \\ Anders Hellström, Sep 14 2015
(Perl) use ntheory ":all"; say $_+1 for grep { next_prime($_+2)-$_ == 18 && $_-prev_prime($_) == 16} @{twin_primes(1e9)}; # Dana Jacobsen, Oct 13 2015
(Perl) use ntheory ":all"; say $_+17 for grep { next_prime($_+0)-$_ == 16 && next_prime($_+18)-$_ == 34} sieve_prime_cluster(1, 1e9, 16, 18, 34); # Dana Jacobsen, Oct 13 2015

Crossrefs

Cf. A014574, A077800 (twin primes), A249674, A256753.

Sequence in context: A031611 A133966 A043671 * A172788 A185573 A185926

Adjacent sequences: A262173 A262174 A262175 * A262177 A262178 A262179

Keyword

nonn

Author

Karl V. Keller, Jr., Sep 13 2015

Status

approved