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A275736 a(n) has base-2 representation with ones in those digit-positions 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 (list; graph; refs; listen; history; text; internal format)
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 zero-based 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 memoization-macro 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
Left inverse of A059590.
Cf. A255411 (indices of zeros).
Cf. also A275732.
Sequence in context: A168068 A163575 A355889 * A276074 A317613 A292628
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Aug 09 2016
STATUS
approved

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Last modified May 24 21:03 EDT 2024. Contains 372781 sequences. (Running on oeis4.)