A175940 Number of ways of writing n=p+f with p a prime and f a factorial.

0, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0, 1, 1, 3, 1, 1, 0, 2, 1, 2, 0, 0, 0, 2, 1, 2, 0, 0, 0, 1, 1, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 0, 1, 1, 3, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 1, 3, 1, 1

Offset

1,4

Comments

Number of partitions of n into the sum of a prime number and a factorial number. Number of decompositions of n into an unordered sum of a prime number and a factorial number.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(29)=2 because 29 has two prime + factorial representations, 5+4! and 23+3!.

Maple

a:= proc(n) local t, k;
       t:= 0;
       for k while k! < n do
         if isprime(n-k!) then t:= t+1 fi
       od;
       t
end proc:
seq(a(n), n=1..100); # Robert Israel, Oct 13 2014

Mathematica

a[n_] := Module[{t = 0, k}, For[k = 1, k! < n, k++, If[PrimeQ[n - k!] , t++]]; t];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 02 2023, after Robert Israel *)

Prog

(PARI)
a(n) = c=0; for(i=1, n, if(isprime(n-i!), c++)); c
vector(100, n, a(n)) \\ Derek Orr, Oct 13 2014

Crossrefs

Cf. A000142, A062602, A175931, A175933.

Sequence in context: A284463 A169758 A175933 * A299236 A374076 A353970

Adjacent sequences: A175937 A175938 A175939 * A175941 A175942 A175943

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 25 2010

Extensions

Edited and entries checked by D. S. McNeil, Nov 26 2010

Status

approved