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 A263675 Numbers that are both averages of consecutive primes and nontrivial prime powers. 3
 4, 9, 64, 81, 625, 1681, 4096, 822649, 1324801, 2411809, 2588881, 2778889, 3243601, 3636649, 3736489, 5527201, 6115729, 6405961, 8720209, 9006001, 12752041, 16056049, 16589329, 18088009, 21743569, 25230529, 29343889, 34586161, 37736449, 39150049 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Intersection of A024675 and A025475. Lesser of consecutive primes is in the sequence A084289. LINKS Robert Israel, Table of n, a(n) for n = 1..1560 Eric Weisstein's World of Mathematics, Interprime EXAMPLE 625 is in this sequence because 625 = 5^4, nontrivial prime power, and 625 = (619+631)/2, with 619 and 631 consecutive primes. MAPLE N:= 10^10: # to get all terms <= N Primes:= select(isprime, [2, seq(i, i=3..isqrt(N), 2)]): S:= select(t -> t - prevprime(t) = nextprime(t)-t, {seq(seq(p^j, j=2..floor(log[p](N))), p=Primes)}): sort(convert(S, list)); # Robert Israel, Dec 27 2015 MATHEMATICA (* version >= 6 *)(#/2 + NextPrime[#]/2) & /@ Select[Prime[Range[5000000]], PrimePowerQ[#/2 + NextPrime[#]/2] &] (* Wouter Meeussen, Oct 26 2015 *) PROG (PARI) {for(i=1, 10^8, if(isprimepower(i)>1&&i==(precprime(i-1)+nextprime(i+1))/2, print1(i, ", ")))} CROSSREFS Cf. A075190, A075277, A075296, A078443, A084289, A130178, A263674, A263676. Sequence in context: A029788 A062826 A201918 * A140483 A124683 A077163 Adjacent sequences:  A263672 A263673 A263674 * A263676 A263677 A263678 KEYWORD nonn AUTHOR Antonio Roldán, Oct 23 2015 STATUS approved

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Last modified August 26 03:38 EDT 2019. Contains 326324 sequences. (Running on oeis4.)