A139034 Prime numbers appearing in A139033.

5, 41, 617, 1913, 3677, 5981, 10337, 16421, 32297, 51341, 72077, 98321, 142421, 212117, 288293, 371237, 457673, 570569, 722669, 899069, 1112513, 1360517, 1614533, 1874633, 2159789, 2451389, 2776289, 3158213, 3555113, 3967277, 4402877, 4878977, 5371781, 5925317

Offset: 1

Author

Zak Seidov, Apr 07 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 2000 terms from Zak Seidov)

Crossrefs

Cf. A139033.

Programs

Maple

s:= proc(n) option remember; `if`(n<1, 0, b(n)^2+s(n-1)) end:
b:= proc(n) option remember; local k, m;
      k:= s(n-1); for m from 1+b(n-1)
      while not isprime(k+m^2) do od; m
    end: b(1):=1:
a:= n-> s(n+1):
seq(a(n), n=1..34);  # Alois P. Heinz, Jan 27 2023

Mathematica

s[n_] := s[n] = If[n < 1, 0, b[n]^2 + s[n - 1]];
b[n_] := b[n] = Module[{k, m}, k = s[n - 1]; For[m = 1 + b[n - 1], !PrimeQ[k + m^2], m++]; m];
b[1] = 1;
a[n_] := s[n + 1];
Table[a[n], {n, 1, 34}] (* Jean-François Alcover, Apr 19 2025, after Alois P. Heinz *)

Formula

a(n) = Sum_{i=1..n+1} A139033(i). - Alois P. Heinz, Jan 27 2023

Extensions

Terms corrected by Alois P. Heinz, Jan 27 2023