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

1,1

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

Links

Table of n, a(n) for n=1..63.

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

Adjacent sequences: A306580 A306581 A306582 * A306584 A306585 A306586

Keyword

nonn

Author

Ivan Stoykov, Feb 25 2019

Extensions

More terms from Giovanni Resta, Feb 27 2019

Status

approved