A257638 Numbers n such that n-25, n-1, n+1 and n+25 are consecutive primes.

232962, 311712, 431832, 435948, 473352, 501342, 525492, 596118, 635388, 665922, 699792, 754182, 842448, 1013502, 1017648, 1036002, 1156848, 1255452, 1284738, 1306692, 1479912, 1516128, 1551732, 1560708, 1595928, 1659348, 1690572, 1745112

Offset

1,1

Comments

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

The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.

The numbers n-25 and n+1 belong to A033560 (p and p+24 are primes) and A098974 (p where p+24 is the next prime).

The numbers n-25 and n-1 belong to A252089 (p and p+26 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

232962 is the average of the four consecutive primes 232937, 232961, 232963, 232987.
311712 is the average of the four consecutive primes 311687, 311711, 311713, 311737.

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-25 and nextprime(i+1) == i+25: print (i, end=', ')

Crossrefs

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

Sequence in context: A237462 A244349 A128484 * A116463 A015331 A250697

Adjacent sequences: A257635 A257636 A257637 * A257639 A257640 A257641

Keyword

nonn

Author

Karl V. Keller, Jr., Nov 04 2015

Status

approved