A089359 Primes which can be partitioned into distinct factorials. 0! and 1! are not considered distinct.

2, 3, 7, 31, 127, 151, 727, 751, 5167, 5791, 5881, 40351, 40471, 41047, 41161, 45361, 45481, 362911, 363751, 368047, 368647, 368791, 403327, 403951, 408241, 408271, 408361, 409081, 3628927, 3629671, 3633991, 3634591, 3669241, 3669847, 3669961

Offset: 1

Author

Amarnath Murthy, Nov 07 2003

Keywords

• nonn

Examples

			From _Seiichi Manyama_, Mar 24 2018: (Start)
n | a(n) |
--+------+------------------
1 |    2 | 2!
2 |    3 | 2! + 1!
3 |    7 | 3! + 1!
4 |   31 | 4! + 3! + 1!
5 |  127 | 5! + 3! + 1!
6 |  151 | 5! + 4! + 3! + 1! (End)
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..16812 (first 1000 terms from Seiichi Manyama)

Crossrefs

Cf. A059590, A088332, A300947, A301593.

Programs

Python

from sympy import isprime
def facbase(k, f):
    return sum(f[i] for i, bi in enumerate(bin(k)[2:][::-1]) if bi == "1")
def auptoN(N): # terms up to N factorial-base digits; 20 generates b-file
    f = [factorial(i) for i in range(1, N+1)]
    return list(filter(isprime, (facbase(k, f) for k in range(2**N))))
print(auptoN(10)) # Michael S. Branicky, Oct 15 2022

Extensions

More terms from Vladeta Jovovic, Nov 08 2003