A255342 Numbers n such that there are exactly two 1's in their factorial base representation (A007623).

3, 7, 8, 11, 15, 21, 25, 26, 29, 30, 34, 37, 38, 41, 43, 44, 47, 51, 55, 56, 59, 63, 69, 75, 79, 80, 83, 87, 93, 99, 103, 104, 107, 111, 117, 121, 122, 125, 126, 130, 133, 134, 137, 139, 140, 143, 144, 148, 156, 160, 162, 166, 169, 170, 173, 174, 178, 181, 182, 185, 187, 188, 191, 193, 194, 197, 198, 202

Offset: 1

Author

Antti Karttunen, Apr 27 2015

Keywords

• nonn
• base

Examples

			The factorial base representation (A007623) of 3 is "11", which contains exactly two 1's, thus 3 is included in the sequence.
The f.b.r. of 7 is "101", with exactly two 1's, thus 7 is included in the sequence.
The f.b.r. of 21 is "311", with exactly two 1's, thus 21 is included in the sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13132

Crossrefs

Cf. A007623, A257511, A255411, A255341, A255343.

Subsequence of A256450.

Subsequence: A038507 (apart from its initial 2 terms).

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, 240}]; Flatten@ Position[s, x_ /; DigitCount[x][[1]] == 2](* Michael De Vlieger, Apr 27 2015, after Alonso del Arte at A007623 *)