A270754 Numbers n such that n - 31, n - 1, n + 1 and n + 31 are consecutive primes.

90438, 258918, 293862, 385740, 426162, 532950, 1073952, 1317192, 1318410, 1401318, 1565382, 1894338, 1986168, 2174772, 2612790, 2764788, 3390900, 3450048, 3618960, 3797250, 3961722, 3973062, 4074870, 4306230, 4648068, 4917360, 5351010, 5460492

Offset: 1

Author

Karl V. Keller, Jr., Mar 22 2016

Keywords

• nonn

Comments

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

The terms ending in 0 are divisible by 30 (cf. A249674).

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

The numbers n - 31 and n + 1 belong to A049481 (p and p + 30 are primes) and A124596 (p where p + 30 is the next prime).

The numbers n - 31 and n - 1 belong to A049489 (p and p + 32 are primes).

Examples

			90438 is the average of the four consecutive primes 90407, 90437, 90439, 90469.
258918 is the average of the four consecutive primes 258887, 258917, 258919, 258949.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..100000
• 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-31 and nextprime(i+1) == i+31 :  print (i,end=', ')