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A257511
Number of 1's in factorial base representation of n (A007623).
17
0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 2, 3, 3, 4, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 2, 3, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 1
OFFSET
0,4
FORMULA
a(0) = 0; for n >= 1, a(n) = A265333(n) + a(A257687(n)). - Antti Karttunen, Aug 29 2016
Other identities and observations. For all n >= 0:
a(n) = A260736(A225901(n)).
a(n) = A001221(A275732(n)) = A001222(A275732(n)).
a(n) = A007814(A275735(n)).
a(n) = A056169(A276076(n)).
a(A007489(n)) = n. [Particularly, A007489(n) gives the position where n first appears.]
a(n) <= A060130(n) <= A034968(n).
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, 0, 120}];
First@ DigitCount[#] & /@ s (* Michael De Vlieger, Apr 27 2015, after Alonso del Arte at A007623 *)
nn = 120; b = Module[{m = 1}, While[Factorial@ m < nn, m++]; MixedRadix[Reverse@ Range[2, m]]]; Table[Count[IntegerDigits[n, b], 1], {n, 0, nn}] (* Michael De Vlieger, Aug 29 2016, Version 10.2 *)
PROG
(Scheme) (define (A257511 n) (let loop ((n n) (i 2) (s 0)) (cond ((zero? n) s) (else (loop (floor->exact (/ n i)) (+ 1 i) (+ s (if (= 1 (modulo n i)) 1 0)))))))
CROSSREFS
Cf. A255411 (numbers n such that a(n) = 0), A255341 (such that a(n) = 1), A255342 (such that a(n) = 2), A255343 (such that a(n) = 3).
Positions of records: A007489.
Cf. also A257510.
Sequence in context: A064875 A216657 A328614 * A039802 A126726 A143656
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Apr 27 2015
STATUS
approved