cp's OEIS Frontend

A263675 Numbers that are both averages of consecutive primes and nontrivial prime powers.

%I A263675 #33 Feb 16 2025 08:33:27
%S A263675 4,9,64,81,625,1681,4096,822649,1324801,2411809,2588881,2778889,
%T A263675 3243601,3636649,3736489,5527201,6115729,6405961,8720209,9006001,
%U A263675 12752041,16056049,16589329,18088009,21743569,25230529,29343889,34586161,37736449,39150049
%N A263675 Numbers that are both averages of consecutive primes and nontrivial prime powers.
%C A263675 Intersection of A024675 and A025475.
%C A263675 Lesser of consecutive primes is in the sequence A084289.
%H A263675 Robert Israel, <a href="/A263675/b263675.txt">Table of n, a(n) for n = 1..1560</a>
%H A263675 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Interprime.html">Interprime</a>
%e A263675 625 is in this sequence because 625 = 5^4, nontrivial prime power, and 625 = (619+631)/2, with 619 and 631 consecutive primes.
%p A263675 N:= 10^10: # to get all terms <= N
%p A263675 Primes:= select(isprime, [2,seq(i,i=3..isqrt(N),2)]):
%p A263675 S:= select(t -> t - prevprime(t) = nextprime(t)-t, {seq(seq(p^j, j=2..floor(log[p](N))),p=Primes)}):
%p A263675 sort(convert(S,list)); # _Robert Israel_, Dec 27 2015
%t A263675 (* version >= 6 *)(#/2 + NextPrime[#]/2) & /@
%t A263675 Select[Prime[Range[5000000]], PrimePowerQ[#/2 + NextPrime[#]/2] &]
%t A263675 (* _Wouter Meeussen_, Oct 26 2015 *)
%o A263675 (PARI) {for(i=1,10^8,if(isprimepower(i)>1&&i==(precprime(i-1)+nextprime(i+1))/2,print1(i,", ")))}
%Y A263675 Cf. A075190, A075277, A075296, A078443, A084289, A130178, A263674, A263676.
%K A263675 nonn
%O A263675 1,1
%A A263675 _Antonio Roldán_, Oct 23 2015