

A275736


a(n) has base2 representation with ones in those digitpositions where n contains ones in its factorial base representation, and zeros in all the other positions.


10



0, 1, 2, 3, 0, 1, 4, 5, 6, 7, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 8, 9, 10, 11, 8, 9, 12, 13, 14, 15, 12, 13, 8, 9, 10, 11, 8, 9, 8, 9, 10, 11, 8, 9, 0, 1, 2, 3, 0, 1, 4, 5, 6, 7, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 4, 5, 6, 7, 4, 5, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 1, 4, 5, 6, 7, 4, 5, 0
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OFFSET

0,3


COMMENTS

Each natural numbers occurs an infinite number of times.
Can be used when computing A275727.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..40320
Index entries for sequences related to binary expansion of n
Index entries for sequences related to factorial base representation


FORMULA

If A257261(n) = 0, then a(n) = 0, otherwise a(n) = A000079(A257261(n)1) + a(A275730(n, A257261(n)1)). [Here A275730(n,p) is a bivariate function that "clears" the digit at zerobased position p in the factorial base representation of n].
Other identities and observations. For all n >= 0:
a(n) = A048675(A275732(n)).
A000120(a(n)) = A257511(n).
a(A007489(n)) = A000225(n).
a(A059590(n)) = n.
a(A255411(n)) = 0.


EXAMPLE

22 has factorial base representation "320" (= A007623(22)), which does not contain any "1". Thus a(22) = 0, as the empty sum is 0.
35 has factorial base representation "1121" (= A007623(35)). Here 1's occur in the following positions, when counted from right (starting with 0 for the least significant position): 0, 2 and 3. Thus a(35) = 2^0 + 2^2 + 2^3 = 1*4*8 = 13.


MATHEMATICA

nn = 120; m = 1; While[Factorial@ m < nn, m++]; m; Map[FromDigits[#, 2] &[IntegerDigits[#, MixedRadix[Reverse@ Range[2, m]]] /. k_ /; k != 1 > 0] &, Range[0, nn]] (* Michael De Vlieger, Aug 11 2016, Version 10.2 *)


PROG

(Scheme, with memoizationmacro definec)
(definec (A275736 n) (cond ((zero? (A257261 n)) 0) (else (+ (A000079 (+ 1 (A257261 n))) (A275736 (A275730bi n ( (A257261 n) 1))))))) ;; Code for A275730bi given in A275730.


CROSSREFS

Cf. A000079, A000120, A000225, A007489, A048675, A257261, A257511, A275727, A275730.
Left inverse of A059590.
Cf. A255411 (indices of zeros).
Cf. also A275732.
Sequence in context: A285320 A168068 A163575 * A276074 A317613 A292628
Adjacent sequences: A275733 A275734 A275735 * A275737 A275738 A275739


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Aug 09 2016


STATUS

approved



