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

%I A263298 #21 Feb 16 2025 08:33:27
%S A263298 19890,43890,157770,400680,436650,609780,681090,797310,924360,978180,
%T A263298 1093200,1116570,1179150,1185930,1313700,1573110,1663350,2001510,
%U A263298 2110290,2163570,2336310,2372370,2408280,2415630,2562690,2877840,2896740,2961900
%N A263298 Numbers n such that n-23, n-1, n+1 and n+23 are consecutive primes.
%C A263298 This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).
%C A263298 From _Michel Marcus_, Oct 15 2015: (Start)
%C A263298 n-23 and n+1 belong to A242476 (p and p+22 are primes).
%C A263298 n-23 and n-1 belong to A033560 (p and p+24 are primes).
%C A263298 (End)
%H A263298 Karl V. Keller, Jr., <a href="/A263298/b263298.txt">Table of n, a(n) for n = 1..10000</a>
%H A263298 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%e A263298 19890 is the average of the four consecutive primes 19867, 19889, 19891, 19913.
%e A263298 43890 is the average of the four consecutive primes 43867, 43889, 43891, 43913.
%t A263298 {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 *)
%o A263298 (Python)
%o A263298 from sympy import isprime,prevprime,nextprime
%o A263298 for i in range(0,5000001,6):
%o A263298   if  isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-23 and nextprime(i+1) == i+23: print (i,end=', ')
%o A263298 (PARI) isok(n) = isprime(n-1) && isprime(n+1) && (precprime(n-2) == n-23) && (nextprime(n+2) == n+23); \\ _Michel Marcus_, Oct 14 2015
%Y A263298 Cf. A014574, A077800 (twin primes), A249674, A256753.
%K A263298 nonn
%O A263298 1,1
%A A263298 _Karl V. Keller, Jr._, Oct 13 2015