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

%I A089359 #25 Oct 15 2022 14:09:10
%S A089359 2,3,7,31,127,151,727,751,5167,5791,5881,40351,40471,41047,41161,
%T A089359 45361,45481,362911,363751,368047,368647,368791,403327,403951,408241,
%U A089359 408271,408361,409081,3628927,3629671,3633991,3634591,3669241,3669847,3669961
%N A089359 Primes which can be partitioned into distinct factorials. 0! and 1! are not considered distinct.
%H A089359 Alois P. Heinz, <a href="/A089359/b089359.txt">Table of n, a(n) for n = 1..16812</a> (first 1000 terms from Seiichi Manyama)
%e A089359 From _Seiichi Manyama_, Mar 24 2018: (Start)
%e A089359 n | a(n) |
%e A089359 --+------+------------------
%e A089359 1 |    2 | 2!
%e A089359 2 |    3 | 2! + 1!
%e A089359 3 |    7 | 3! + 1!
%e A089359 4 |   31 | 4! + 3! + 1!
%e A089359 5 |  127 | 5! + 3! + 1!
%e A089359 6 |  151 | 5! + 4! + 3! + 1! (End)
%o A089359 (Python)
%o A089359 from sympy import isprime
%o A089359 def facbase(k, f):
%o A089359     return sum(f[i] for i, bi in enumerate(bin(k)[2:][::-1]) if bi == "1")
%o A089359 def auptoN(N): # terms up to N factorial-base digits; 20 generates b-file
%o A089359     f = [factorial(i) for i in range(1, N+1)]
%o A089359     return list(filter(isprime, (facbase(k, f) for k in range(2**N))))
%o A089359 print(auptoN(10)) # _Michael S. Branicky_, Oct 15 2022
%Y A089359 Cf. A059590, A088332, A300947, A301593.
%K A089359 nonn
%O A089359 1,1
%A A089359 _Amarnath Murthy_, Nov 07 2003
%E A089359 More terms from _Vladeta Jovovic_, Nov 08 2003