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

Author

Karl V. Keller, Jr., Nov 04 2015

Keywords

• nonn

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).

Examples

			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.
		

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

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=', ')