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

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

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