A262176 Numbers k such that k-17, k-1, k+1 and k+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

Author

Karl V. Keller, Jr., Sep 13 2015

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Twin Primes

Crossrefs

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

Programs

Mathematica

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

PARI

list(l)=for(i=1,l,my(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

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=', ')