A309489 Numbers k such that the sum of digits in odd places is equal to the sum of digits in even places in k!.

11, 18, 20, 25, 27, 28, 32, 35, 41, 43, 51, 57, 60, 68, 72, 74, 80, 102, 105, 107, 113, 121, 122, 138, 140, 145, 156, 161, 166, 171, 228, 233, 245, 282, 301, 307, 308, 311, 315, 329, 333, 335, 340, 347, 349, 351, 353, 366, 386, 412, 420, 454, 469, 478

Offset: 1

Author

Daniel Starodubtsev, Aug 04 2019

Keywords

• nonn
• base

Comments

Numbers k such that A000142(k) is a term of A135499. - Michel Marcus, Aug 04 2019

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000142 (n!), A135499.

Programs

Mathematica

aQ[n_] := Total[(d = IntegerDigits[n!])[[1;;-1;;2]]] == Total[d[[2;;-1;;2]]]; Select[Range[500], aQ] (* Amiram Eldar, Aug 04 2019 *)
sdoeQ[n_]:=With[{nf=IntegerDigits[n!]},Total[Take[nf,{1,-1,2}]]==Total[Take[nf,{2,-1,2}]]]; Select[Range[500],sdoeQ] (* Harvey P. Dale, Jun 04 2025 *)

PARI

isok(k) = {my(d = digits(k!), so=0, se=0); for (i=1, #d, if (i%2, so += d[i], se += d[i])); so == se; } \\ Michel Marcus, Aug 04 2019

Python

def c(n): s = str(n); return sum(map(int, s[::2])) == sum(map(int, s[1::2]))
def afind(limit):
    k, factk = 1, 1
    while k <= limit:
        if c(factk): print(k, end=", ")
        k += 1; factk *= k
afind(500) # Michael S. Branicky, Nov 18 2021