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

1,1

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)

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Primes

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A256653 A186957 A236907 * A237564 A171353 A175590

Adjacent sequences: A263295 A263296 A263297 * A263299 A263300 A263301

Keyword

nonn

Author

Karl V. Keller, Jr., Oct 13 2015

Status

approved