A338446 Numbers that are sums of consecutive odd primes.

3, 5, 7, 8, 11, 12, 13, 15, 17, 18, 19, 23, 24, 26, 29, 30, 31, 36, 37, 39, 41, 42, 43, 47, 48, 49, 52, 53, 56, 59, 60, 61, 67, 68, 71, 72, 73, 75, 78, 79, 83, 84, 88, 89, 90, 95, 97, 98, 100, 101, 102, 103, 107, 109, 112, 113, 119, 120, 121, 124, 127, 128, 131, 132, 137

Offset: 1

Author

Ilya Gutkovskiy, Oct 28 2020

Keywords

• nonn

Examples

			67 is in the sequence because 67 = 7 + 11 + 13 + 17 + 19.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007504, A034707, A050936, A053790, A065091, A071148.

Programs

Maple

q:= proc(n) local p, q, s; p, q, s:= prevprime(n+1)$3;
      do if p=2 then return false
       elif s=n then return true
       elif sAlois P. Heinz, Oct 31 2020

Mathematica

okQ[n_] := Module[{p, q, s}, {p, q, s} = Table[NextPrime[n + 1, -1], {3}]; While[True, Which[
     p == 2, Return@ False,
     s == n, Return@ True,
     s < n, p = NextPrime[p, -1]; s = s + p,
     True, s = s - q; q = NextPrime[q, -1]]]];
Select[Range[3, 150], okQ] (* Jean-François Alcover, Feb 21 2022, after Alois P. Heinz *)

Python

from sympy import prevprime
def ok(n):
    if n < 2: return False
    p, q, s = [prevprime(n+1)] * 3
    while True:
        if p == 2: return False
        if s == n: return True
        elif s < n: p = prevprime(p); s += p
        else: s -= q; q = prevprime(q)
print([k for k in range(150) if ok(k)]) # Michael S. Branicky, Feb 21 2022 after Alois P. Heinz