A263298 Numbers n such that n-23, n-1, n+1 and n+23 are consecutive primes.

19890, 43890, 157770, 400680, 436650, 609780, 681090, 797310, 924360, 978180, 1093200, 1116570, 1179150, 1185930, 1313700, 1573110, 1663350, 2001510, 2110290, 2163570, 2336310, 2372370, 2408280, 2415630, 2562690, 2877840, 2896740, 2961900

Offset: 1

Author

Karl V. Keller, Jr., Oct 13 2015

Keywords

• nonn

Comments

This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).

From Michel Marcus, Oct 15 2015: (Start)

n-23 and n+1 belong to A242476 (p and p+22 are primes).

n-23 and n-1 belong to A033560 (p and p+24 are primes).

(End)

Examples

			19890 is the average of the four consecutive primes 19867, 19889, 19891, 19913.
43890 is the average of the four consecutive primes 43867, 43889, 43891, 43913.
		

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

{p, q, r, s} = {2, 3, 5, 7};lst={}; While[p<5000000, If[Differences[{p, q, r, s}]=={22, 2, 22}, AppendTo[lst, q + 1]]; {p, q, r, s}={q, r, s,NextPrime@s}]; lst (* Vincenzo Librandi, Oct 14 2015 *)

PARI

isok(n) = isprime(n-1) && isprime(n+1) && (precprime(n-2) == n-23) && (nextprime(n+2) == n+23); \\ Michel Marcus, Oct 14 2015

Python

from sympy import isprime,prevprime,nextprime
for i in range(0,5000001,6):
  if  isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-23 and nextprime(i+1) == i+23: print (i,end=', ')