

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



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:


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)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



