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

1,1

Links

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

Example

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

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 s<n then p:= prevprime(p); s:= s+p;
                else s:= s-q; q:= prevprime(q)
         fi
      od
    end:
select(q, [$3..150])[];  # Alois 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 *)

Prog

(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

Crossrefs

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

Sequence in context: A258025 A239419 A195439 * A190719 A187224 A106252

Adjacent sequences: A338443 A338444 A338445 * A338447 A338448 A338449

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 28 2020

Status

approved