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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
OFFSET
1,1
COMMENTS
It can be proved that any number in the gap between n! + (n-1)! + (n-2)! + ... + 2! + 1! + 0! and (n+1)! - (n! + (n-1)! + (n-2)! + ... + 2! + 1! + 0!) is in this sequence.
0! and 1! are treated as distinct. - Bernard Schott, Feb 25 2019
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. A000142 and A007489.
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).
Sequence in context: A097932 A031300 A111019 * A048035 A048015 A061082
KEYWORD
nonn
AUTHOR
Ivan Stoykov, Feb 25 2019
EXTENSIONS
More terms from Giovanni Resta, Feb 27 2019
STATUS
approved