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

1,1

Links

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

Example

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)

Prog

(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

Crossrefs

Cf. A059590, A088332, A300947, A301593.

Sequence in context: A163075 A265113 A228171 * A239892 A267487 A343733

Adjacent sequences: A089356 A089357 A089358 * A089360 A089361 A089362

Keyword

nonn

Author

Amarnath Murthy, Nov 07 2003

Extensions

More terms from Vladeta Jovovic, Nov 08 2003

Status

approved