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

1,1

Comments

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

Links

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

Example

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.

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;

Crossrefs

Cf. A001414, A246547.

Sequence in context: A119889 A038956 A309291 * A040123 A296936 A038883

Adjacent sequences: A343120 A343121 A343122 * A343124 A343125 A343126

Keyword

nonn

Author

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

Status

approved