cp's OEIS Frontend

A258088 Numbers n such that n is the average of four consecutive primes n-5, n-1, n+1 and n+5.

%I A258088 #42 May 22 2025 10:21:43
%S A258088 12,18,42,102,108,228,312,462,858,882,1092,1302,1428,1488,1872,1998,
%T A258088 2688,3462,4518,4788,5232,5652,6828,7878,8292,10458,13692,13878,15732,
%U A258088 16062,16068,16188,17388,19422,19428,20748,21018,21318,22278,23058
%N A258088 Numbers n such that n is the average of four consecutive primes n-5, n-1, n+1 and n+5.
%C A258088 Previous name was: Numbers n such that n is the average of some twin prime pair p, q (q=p+2) (i.e., n=p+1=q-1) where p-4, p, q, and q+4 are consecutive primes.
%C A258088 This is a subsequence of A014574 (average of twin prime pairs) and A256753.
%H A258088 Karl V. Keller, Jr., <a href="/A258088/b258088.txt">Table of n, a(n) for n = 1..10000</a>
%H A258088 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%F A258088 a(n) = A052378(n) + 5. - _Karl V. Keller, Jr._, Jul 17 2015
%e A258088 12 is the average of the four consecutive primes 7, 11, 13, 17.
%e A258088 18 is the average of the four consecutive primes 13, 17, 19, 23.
%t A258088 a={};Do[If[Prime[x + 3] - Prime[x]==10, AppendTo[a, Prime[x]+ 5]], {x, 1, 4000}]; a (* _Vincenzo Librandi_, Jul 18 2015 *)
%t A258088 Mean/@Select[Partition[Prime[Range[3000]],4,1],Differences[#]=={4,2,4}&] (* _Harvey P. Dale_, Sep 18 2018 *)
%o A258088 (Python)
%o A258088 from sympy import isprime,prevprime,nextprime
%o A258088 for i in range(0,50001,2):
%o A258088   if isprime(i-1) and isprime(i+1):
%o A258088     if prevprime(i-1) == i-5 and nextprime(i+1) == i+5: print (i,end=', ')
%o A258088 (PARI) is(n)=isprime(n-5)&&isprime(n-1)&&isprime(n+1)&&isprime(n+5) \\ _Charles R Greathouse IV_, Aug 28 2015
%Y A258088 Cf. A014574, A052378, A077800 (twin primes), A256753.
%K A258088 nonn
%O A258088 1,1
%A A258088 _Karl V. Keller, Jr._, May 19 2015
%E A258088 New name from _Karl V. Keller, Jr._, Jul 21 2015