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

1,1

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).

Links

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

Eric Weisstein's World of Mathematics, Twin Primes

Example

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.

Mathematica

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

Prog

(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=', ')

Crossrefs

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

Sequence in context: A069372 A157839 A237808 * A295472 A162765 A186879

Adjacent sequences: A271346 A271347 A271348 * A271350 A271351 A271352

Keyword

nonn

Author

Karl V. Keller, Jr., Apr 04 2016

Status

approved