A271349 Numbers n such that n - 35, n - 1, n + 1 and n + 35 are consecutive primes.

276672, 558828, 1050852, 1278288, 1486908, 1625418, 2536308, 2538918, 2690958, 2731242, 3015162, 3252678, 3268338, 3508278, 3711612, 4233708, 4575912, 4717962, 5004402, 5108352, 5404032, 5482782, 5519082, 5525328, 5640918, 5654358, 5995818

Offset: 1

Author

Karl V. Keller, Jr., Apr 04 2016

Keywords

• nonn

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.

The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.

The numbers n - 35 and n + 1 belong to A252091 (p and p + 34 are primes) and A134116 (p such that p + 34 is the next prime).

The numbers n - 35 and n - 1 belong to A156104 (p and p + 36 are primes).

Examples

			276672 is the average of the four consecutive primes 276637, 276671, 276673, 276707.
558828 is the average of the four consecutive primes 558793, 558827, 558829, 558863.
		

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), A256753.

Programs

Mathematica

Select[Partition[Prime[Range[500000]],4,1],Differences[#]=={34,2,34}&] [[All, 2]]+1 (* Harvey P. Dale, Oct 11 2017 *)

Python

from sympy import isprime,prevprime,nextprime
for i in range(0,1000001,6):
  if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-35 and nextprime(i+1) == i+35 :  print (i,end=', ')