A306583 Positive integers that cannot be represented as a sum or difference of factorials of distinct integers.

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

Author

Ivan Stoykov, Feb 25 2019

Keywords

• nonn

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

Examples

			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.
		

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).

Programs

Mathematica

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

Extensions

More terms from Giovanni Resta, Feb 27 2019