A265651 Numbers n such that n-29, n-1, n+1 and n+29 are consecutive primes.

14592, 84348, 151938, 208962, 241392, 254490, 397182, 420192, 494442, 527700, 549978, 581982, 637200, 641550, 712602, 729330, 791628, 850302, 975552, 995052, 1086558, 1107852, 1157670, 1245450, 1260798, 1286148, 1494510, 1555290, 1608912

Offset: 1

Author

Karl V. Keller, Jr., Dec 11 2015

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-29 and n+1 belong to A252090 (p and p+28 are primes) and A124595 (p where p+28 is the next prime).

The numbers n-29 and n-1 belong to A049481 (p and p+30 are primes).

Examples

			14592 is the average of the four consecutive primes 14563, 14591, 14593, 14621.
84348 is the average of the four consecutive primes 84319, 84347, 84349, 84377.
		

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

Select[Prime@Range@100000, NextPrime[#, {1, 2, 3}] == {28, 30, 58} + # &] + 29 (* Vincenzo Librandi, Dec 12 2015 *)
Mean/@Select[Partition[Prime[Range[125000]],4,1],Differences[#]=={28,2,28}&] (* Harvey P. Dale, May 02 2016 *)

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-29 and nextprime(i+1) == i+29 :  print (i,end=', ')