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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 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 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 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: A168068 A163575 A355889 * A276074 A317613 A292628 Adjacent sequences: A275733 A275734 A275735 * A275737 A275738 A275739 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.)