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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 17 13:00 EDT 2019. Contains 327131 sequences. (Running on oeis4.)