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A089359
Primes which can be partitioned into distinct factorials. 0! and 1! are not considered distinct.
5
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 07 2003
EXTENSIONS
More terms from Vladeta Jovovic, Nov 08 2003
STATUS
approved