A341945 Number of partitions of n into 2 primes (counting 1 as a prime).

1, 1, 2, 1, 2, 1, 2, 1, 2, 0, 2, 1, 3, 1, 2, 0, 3, 1, 3, 1, 3, 0, 4, 1, 3, 0, 2, 0, 4, 1, 3, 1, 4, 0, 4, 0, 3, 1, 3, 0, 5, 1, 4, 1, 4, 0, 6, 1, 4, 0, 3, 0, 6, 1, 3, 0, 4, 0, 7, 1, 4, 1, 5, 0, 6, 0, 3, 1, 5, 0, 7, 1, 6, 1, 5, 0, 7, 0, 5, 1, 5, 0, 9, 1, 5, 0, 4, 0, 10

Offset: 2

Author

Ilya Gutkovskiy, Feb 24 2021

Keywords

• nonn
• look

Comments

Number of partitions of n into 2 noncomposite numbers, A008578. - Antti Karttunen, Dec 13 2021

Links

• Antti Karttunen, Table of n, a(n) for n = 2..20000

Crossrefs

Cf. A001031, A008578, A034891, A061358, A341946, A341947, A341948, A341949, A341950, A341951.

Programs

Maple

b:= proc(n, i) option remember; series(`if`(n=0, 1,
     `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
     `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 3)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 2):
seq(a(n), n=2..90);  # Alois P. Heinz, Feb 24 2021

Mathematica

a[n_] := If[2 == n, 1, Module[{s = 0}, For[p = 2, True, p = NextPrime[p], If[p > n-p, Return[s + Boole[PrimeQ[n-1]]], s += Boole[PrimeQ[n-p]]]]]];
Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Jan 03 2022, after Antti Karttunen *)

PARI

A341945(n) = if(2==n,1,my(s=0); forprime(p=2,,if(p>(n-p), return(s+isprime(n-1)), s += isprime(n-p)))); \\ Antti Karttunen, Dec 13 2021