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
Keywords
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)
Programs
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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
Comments