%I #30 Jul 01 2019 02:01:56
%S 11,12,13,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
%T 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,
%U 78,79,80,81,82,83,84,85,107,108,109,131,132,133,155,156,157
%N Positive integers that cannot be represented as a sum or difference of factorials of distinct integers.
%C 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 0! and 1! are treated as distinct. - _Bernard Schott_, Feb 25 2019
%e 10 can be represented as 10 = 0! + 1! + 2! + 3!, so it is not a term.
%e 11 cannot be represented as a sum or a difference of factorials, so it is a term.
%t Complement[Range[160], Total[# Range[0, 5]!] & /@ (IntegerDigits[ Range[3^6 - 1], 3, 6] - 1)] (* _Giovanni Resta_, Feb 27 2019 *)
%Y Cf. A000142 and A007489.
%Y 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 nonn
%O 1,1
%A _Ivan Stoykov_, Feb 25 2019
%E More terms from _Giovanni Resta_, Feb 27 2019