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A343123 Primes p such that the sum of A001414(k) for k strictly between p and the following prime is a proper prime power (a term of A246547).

%I A343123 #12 May 08 2021 11:30:13
%S A343123 3,13,17,19,239,269,457,751,1091,1319,1871,2129,2141,2341,2549,2683,
%T A343123 2969,3167,3359,3671,3821,4091,4799,5437,5843,6299,6551,6779,7559,
%U A343123 8387,8999,9239,9419,10529,11057,11717,11777,12071,13309,13901,17027,17203,18047,18311,18521,21139,23831,26249,26861
%N A343123 Primes p such that the sum of A001414(k) for k strictly between p and the following prime is a proper prime power (a term of A246547).
%C A343123 Primes prime(k) such that Sum_{prime(k) < j < prime(k+1)} A001414(j) is in A246547.
%H A343123 Robert Israel, <a href="/A343123/b343123.txt">Table of n, a(n) for n = 1..3000</a>
%e A343123 a(4) = 19 is a term because 19 and 23 are consecutive primes with Sum_{19 < j < 23} A001414(j) = 9+10+13 = 32 = 2^5.
%p A343123 spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
%p A343123 R:= NULL: count:= 0: p:= 2:
%p A343123 while count < 100 do
%p A343123   q:= p; p:= nextprime(p);
%p A343123   L:= ifactors(add(spf(i),i=q+1..p-1))[2];
%p A343123   if nops(L) = 1 and L[1][2]>1 then
%p A343123     count:= count+1; R:= R, q;
%p A343123   fi
%p A343123 od:
%p A343123 R;
%Y A343123 Cf. A001414, A246547.
%K A343123 nonn
%O A343123 1,1
%A A343123 _J. M. Bergot_ and _Robert Israel_, Apr 05 2021