A255341 Numbers n such that there is exactly one 1 in their factorial base representation (A007623).

1, 2, 5, 6, 10, 13, 14, 17, 19, 20, 23, 24, 28, 36, 40, 42, 46, 49, 50, 53, 54, 58, 61, 62, 65, 67, 68, 71, 73, 74, 77, 78, 82, 85, 86, 89, 91, 92, 95, 97, 98, 101, 102, 106, 109, 110, 113, 115, 116, 119, 120, 124, 132, 136, 138, 142, 168, 172, 180, 184, 186, 190, 192, 196, 204, 208, 210

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..13069

Example

The factorial base representation (A007623) of 5 is "21", which contains exactly one 1, thus 5 is included in the sequence.
The f.b.r. of 23 is "321", with only one 1, thus 23 is included in the sequence.
The f.b.r. of 24 is "1000", with only one 1, thus 24 is included in the sequence.

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, 210}]; {0}~Join~Flatten@ Position[s, x_ /; DigitCount[x][[1]] == 1] (* Michael De Vlieger, Apr 27 2015, after Alonso del Arte at A007623 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A255341 (MATCHING-POS 1 0 (lambda (n) (= 1 (A257511 n)))))

Crossrefs

Cf. A007623, A257511, A255411, A255342, A255343.

Subsequence of A256450.

Subsequences: A000142, A033312 (apart from its zero-terms).

Sequence in context: A162340 A212016 A212015 * A089269 A047440 A255055

Adjacent sequences: A255338 A255339 A255340 * A255342 A255343 A255344

Keyword

nonn,base

Author

Antti Karttunen, Apr 27 2015

Status

approved