This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A306583 #30 Jul 01 2019 02:01:56 %S A306583 11,12,13,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54, %T A306583 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77, %U A306583 78,79,80,81,82,83,84,85,107,108,109,131,132,133,155,156,157 %N A306583 Positive integers that cannot be represented as a sum or difference of factorials of distinct integers. %C A306583 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. %C A306583 0! and 1! are treated as distinct. - _Bernard Schott_, Feb 25 2019 %e A306583 10 can be represented as 10 = 0! + 1! + 2! + 3!, so it is not a term. %e A306583 11 cannot be represented as a sum or a difference of factorials, so it is a term. %t A306583 Complement[Range[160], Total[# Range[0, 5]!] & /@ (IntegerDigits[ Range[3^6 - 1], 3, 6] - 1)] (* _Giovanni Resta_, Feb 27 2019 *) %Y A306583 Cf. A000142 and A007489. %Y A306583 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). %K A306583 nonn %O A306583 1,1 %A A306583 _Ivan Stoykov_, Feb 25 2019 %E A306583 More terms from _Giovanni Resta_, Feb 27 2019