A341982 Number of ways to write n as an ordered sum of 2 primes (counting 1 as a prime).

1, 2, 3, 2, 3, 2, 4, 2, 3, 0, 4, 2, 5, 2, 4, 0, 6, 2, 6, 2, 5, 0, 8, 2, 5, 0, 4, 0, 8, 2, 6, 2, 7, 0, 8, 0, 5, 2, 6, 0, 10, 2, 8, 2, 7, 0, 12, 2, 8, 0, 6, 0, 12, 2, 6, 0, 7, 0, 14, 2, 7, 2, 10, 0, 12, 0, 6, 2, 10, 0, 14, 2, 11, 2, 10, 0, 14, 0, 10, 2, 9, 0, 18, 2, 9, 0, 8

Offset: 2

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A008578, A073610, A096139, A280917, A283762, A341945, A341973, A341983, A341984.

Programs

Maple

b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
      `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 3)
    end:
a:= n-> coeff(b(n), x, 2):
seq(a(n), n=2..88);  # Alois P. Heinz, Feb 24 2021

Mathematica

nmax = 88; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^2, {x, 0, nmax}], x] // Drop[#, 2] &

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^2.