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 A332017 a(n) is the sum of the squares of the lengths of the runs of consecutive equal digits in the binary representation of n. 1
 0, 1, 2, 4, 5, 3, 5, 9, 10, 6, 4, 6, 8, 6, 10, 16, 17, 11, 7, 9, 7, 5, 7, 11, 13, 9, 7, 9, 13, 11, 17, 25, 26, 18, 12, 14, 10, 8, 10, 14, 12, 8, 6, 8, 10, 8, 12, 18, 20, 14, 10, 12, 10, 8, 10, 14, 18, 14, 12, 14, 20, 18, 26, 36, 37, 27, 19, 21, 15, 13, 15, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(0) = 0 by convention. Every nonnegative number k appears A006456(k) times in the sequence, the last occurrence being at index A000975(k). LINKS Rémy Sigrist, Table of n, a(n) for n = 0..8192 Index entries for sequences related to binary expansion of n FORMULA a(n) = Sum_{k = 1..A005811(n)} A101211(n, k)^2. a(A000975(k)) = k for any k >= 0. a(2^k-1) = k^2 for any k >= 0. a(2^k) = k^2+1 for any k >= 0. EXAMPLE For n = 49: - the binary representation of 49 is "110001", - we have a run of 2 1's followed by a run of 3 0's followed by a run of 1 1's, - so a(49) = 2^2 + 3^2 + 1^2 = 14. PROG (PARI) a(n) = { my (v=0); while (n, my (r=valuation(n+(n%2), 2)); v+=r^2; n\=2^r); v } CROSSREFS Cf. A000975, A005811, A006456, A101211. Sequence in context: A021807 A284561 A061728 * A276127 A182115 A362962 Adjacent sequences: A332014 A332015 A332016 * A332018 A332019 A332020 KEYWORD nonn,look,base AUTHOR Rémy Sigrist, Feb 04 2020 STATUS approved

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Last modified April 20 10:17 EDT 2024. Contains 371814 sequences. (Running on oeis4.)