A263298 - OEIS

%I #21 Feb 16 2025 08:33:27

%S 19890,43890,157770,400680,436650,609780,681090,797310,924360,978180,

%T 1093200,1116570,1179150,1185930,1313700,1573110,1663350,2001510,

%U 2110290,2163570,2336310,2372370,2408280,2415630,2562690,2877840,2896740,2961900

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

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

%C From _Michel Marcus_, Oct 15 2015: (Start)

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

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

%C (End)

%H Karl V. Keller, Jr., <a href="/A263298/b263298.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>

%e 19890 is the average of the four consecutive primes 19867, 19889, 19891, 19913.

%e 43890 is the average of the four consecutive primes 43867, 43889, 43891, 43913.

%t {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 (Python)

%o from sympy import isprime,prevprime,nextprime

%o for i in range(0,5000001,6):

%o   if  isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-23 and nextprime(i+1) == i+23: print (i,end=', ')

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

%K nonn,changed

%O 1,1

%A _Karl V. Keller, Jr._, Oct 13 2015