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).

3, 13, 17, 19, 239, 269, 457, 751, 1091, 1319, 1871, 2129, 2141, 2341, 2549, 2683, 2969, 3167, 3359, 3671, 3821, 4091, 4799, 5437, 5843, 6299, 6551, 6779, 7559, 8387, 8999, 9239, 9419, 10529, 11057, 11717, 11777, 12071, 13309, 13901, 17027, 17203, 18047, 18311, 18521, 21139, 23831, 26249, 26861

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 05 2021

Keywords

• nonn

Comments

Primes prime(k) such that Sum_{prime(k) < j < prime(k+1)} A001414(j) is in A246547.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A001414, A246547.

Programs

Maple

spf:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
R:= NULL: count:= 0: p:= 2:
while count < 100 do
  q:= p; p:= nextprime(p);
  L:= ifactors(add(spf(i),i=q+1..p-1))[2];
  if nops(L) = 1 and L[1][2]>1 then
    count:= count+1; R:= R, q;
  fi
od:
R;