

A306583


Positive integers that cannot be represented as a sum or difference of factorials of distinct integers.


0



11, 12, 13, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 107, 108, 109, 131, 132, 133, 155, 156, 157
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OFFSET

1,1


COMMENTS

It can be proved that any number in the gap between n! + (n1)! + (n2)! + ... + 2! + 1! + 0! and (n+1)!  (n! + (n1)! + (n2)! + ... + 2! + 1! + 0!) is in this sequence.


LINKS



EXAMPLE

10 can be represented as 10 = 0! + 1! + 2! + 3!, so it is not a term.
11 cannot be represented as a sum or a difference of factorials, so it is a term.


MATHEMATICA

Complement[Range[160], Total[# Range[0, 5]!] & /@ (IntegerDigits[ Range[3^6  1], 3, 6]  1)] (* Giovanni Resta, Feb 27 2019 *)


CROSSREFS

Cf. A059589 (Sums of factorials of distinct integers with 0! and 1! treated as distinct), A059590 (Sums of factorials of distinct integers with 0! and 1! treated as identical), A005165 (Alternating factorials).


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



