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A263675 Numbers that are both averages of consecutive primes and nontrivial prime powers. 3

%I

%S 4,9,64,81,625,1681,4096,822649,1324801,2411809,2588881,2778889,

%T 3243601,3636649,3736489,5527201,6115729,6405961,8720209,9006001,

%U 12752041,16056049,16589329,18088009,21743569,25230529,29343889,34586161,37736449,39150049

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

%C Intersection of A024675 and A025475.

%C Lesser of consecutive primes is in the sequence A084289.

%H Robert Israel, <a href="/A263675/b263675.txt">Table of n, a(n) for n = 1..1560</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Interprime.html">Interprime</a>

%e 625 is in this sequence because 625 = 5^4, nontrivial prime power, and 625 = (619+631)/2, with 619 and 631 consecutive primes.

%p N:= 10^10: # to get all terms <= N

%p Primes:= select(isprime, [2,seq(i,i=3..isqrt(N),2)]):

%p S:= select(t -> t - prevprime(t) = nextprime(t)-t, {seq(seq(p^j, j=2..floor(log[p](N))),p=Primes)}):

%p sort(convert(S,list)); # _Robert Israel_, Dec 27 2015

%t (* version >= 6 *)(#/2 + NextPrime[#]/2) & /@

%t Select[Prime[Range[5000000]], PrimePowerQ[#/2 + NextPrime[#]/2] &]

%t (* _Wouter Meeussen_, Oct 26 2015 *)

%o (PARI) {for(i=1,10^8,if(isprimepower(i)>1&&i==(precprime(i-1)+nextprime(i+1))/2,print1(i,", ")))}

%Y Cf. A075190, A075277, A075296, A078443, A084289, A130178, A263674, A263676.

%K nonn

%O 1,1

%A _Antonio Roldán_, Oct 23 2015

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)