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

1,1

Links

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

Example

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.

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A255342 (MATCHING-POS 1 0 (lambda (n) (= 2 (A257511 n)))))

Crossrefs

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

Subsequence of A256450.

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

Sequence in context: A069122 A278519 A007970 * A332572 A134258 A028972

Adjacent sequences: A255339 A255340 A255341 * A255343 A255344 A255345

Keyword

nonn,base

Author

Antti Karttunen, Apr 27 2015

Status

approved