A273356 Numbers n such that n - 49, n - 1, n + 1, n + 49 are consecutive primes.

913638, 2763882, 4500492, 6220518, 6473148, 13884468, 15131982, 15729942, 19671930, 20494602, 21372888, 23791350, 25541028, 29535348, 30787788, 30906768, 32085372, 34128168, 34139802, 34550430, 35989980, 37473180, 37784310, 38106372

Offset: 1

Author

Karl V. Keller, Jr., May 20 2016

Keywords

• nonn

Comments

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

The terms ending in 0 belong to A249674 (divisible by 30).

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

The numbers n - 49 and n + 1 belong to A134123 (p such that p + 48 is the next prime).

The numbers n - 49 and n - 1 belong to A062284 (p and p + 50 are primes).

Examples

			913638 is the average of the four consecutive primes 913589, 913637, 913639, 913687.
2763882 is the average of the four consecutive primes 2763833, 2763881, 2763883, 2763931.
		

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

Mean/@Select[Partition[Prime[Range[2325200]],4,1],Differences[#]=={48,2,48}&] (* Harvey P. Dale, Feb 10 2024 *)

PARI

is(n)=isprime(n-1) && isprime(n+1) && precprime(n-2)==n-49 && nextprime(n+2)==n+49 \\ Charles R Greathouse IV, Jun 08 2016

Python

from sympy import isprime,prevprime,nextprime
for i in range(0,60000001,6):
  if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-49 and nextprime(i+1) == i+49: print (i,end=', ')