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

1,1

Links

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

Example

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.

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 *)

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A255343 (MATCHING-POS 1 0 (lambda (n) (= 3 (A257511 n)))))
(Python)
def fbr(n, p=2): # per Indranil Ghosh in A007623
    return n if n<p else fbr(n//p, p+1)*10 + n%p
def ok(n): return str(fbr(n)).count('1') == 3
print(list(filter(ok, range(442)))) # Michael S. Branicky, Sep 27 2021

Crossrefs

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

Subsequence of A256450.

Sequence in context: A115148 A022701 A276003 * A108107 A340237 A216168

Adjacent sequences: A255340 A255341 A255342 * A255344 A255345 A255346

Keyword

nonn,base

Author

Antti Karttunen, Apr 27 2015

Status

approved