A255343 Numbers n such that there are exactly three 1's in their factorial base representation (A007623).

9, 27, 31, 32, 35, 39, 45, 57, 81, 105, 123, 127, 128, 131, 135, 141, 145, 146, 149, 150, 154, 157, 158, 161, 163, 164, 167, 171, 175, 176, 179, 183, 189, 195, 199, 200, 203, 207, 213, 219, 223, 224, 227, 231, 237, 249, 267, 271, 272, 275, 279, 285, 297, 321, 345, 369, 387, 391, 392, 395, 399, 405, 417, 441

Offset: 1

Author

Antti Karttunen, Apr 27 2015

Keywords

• nonn
• base

Examples

			The factorial base representation (A007623) of 9 is "111", which contains exactly three 1's, thus 3 is included in the sequence.
The f.b.r. of 27 is "1011", with exactly three 1's, thus 27 is included in the sequence.
The f.b.r. of 81 is "3111", with exactly three 1's, thus 81 is included in the sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6769

Crossrefs

Cf. A007623, A257511, A255411, A255341, A255342.

Subsequence of A256450.

Programs

Mathematica

factBaseIntDs[n_] := Module[{m, i, len, dList, currDigit}, i = 1; While[n > i!, i++]; m = n; len = i; dList = Table[0, {len}]; Do[currDigit = 0; While[m >= j!, m = m - j!; currDigit++]; dList[[len - j + 1]] = currDigit, {j, i, 1, -1}]; If[dList[[1]] == 0, dList = Drop[dList, 1]]; dList]; s = Table[FromDigits[factBaseIntDs[n]], {n, 480}]; Flatten@ Position[s, x_ /; DigitCount[x][[1]] == 3](* Michael De Vlieger, Apr 27 2015, after Alonso del Arte at A007623 *)

Python

def fbr(n, p=2): # per Indranil Ghosh in A007623
    return n if n
Michael S. Branicky, Sep 27 2021