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A263298
Numbers n such that n-23, n-1, n+1 and n+23 are consecutive primes.
1
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
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
KEYWORD
nonn
AUTHOR
Karl V. Keller, Jr., Oct 13 2015
STATUS
approved