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 A292596 a(1) = a(2) = 0; for n > 2, a(n) = A010051(n) + 2*a(floor(n/2)). 4
 0, 0, 1, 0, 1, 2, 3, 0, 0, 2, 3, 4, 5, 6, 6, 0, 1, 0, 1, 4, 4, 6, 7, 8, 8, 10, 10, 12, 13, 12, 13, 0, 0, 2, 2, 0, 1, 2, 2, 8, 9, 8, 9, 12, 12, 14, 15, 16, 16, 16, 16, 20, 21, 20, 20, 24, 24, 26, 27, 24, 25, 26, 26, 0, 0, 0, 1, 4, 4, 4, 5, 0, 1, 2, 2, 4, 4, 4, 5, 16, 16, 18, 19, 16, 16, 18, 18, 24, 25, 24, 24, 28, 28, 30, 30, 32, 33, 32, 32, 32, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS 1-bits in base-2 expansion of a(n) indicate the positions of odd primes in the sequence [n, floor(n/2), floor(n/4), ..., 1]. LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(1) = a(2) = 0; for n > 2, a(n) = A010051(n) + 2*a(floor(n/2)). Other identities. For all n >= 1: a(n) + A292597(n) = n. A000120(a(n)) = A292598(n). A007814(1+a(n)) <= A007814(1+n). PROG (Scheme, with memoization-macro definec) (definec (A292596 n) (if (<= n 2) 0 (+ (A010051 n) (* 2 (A292596 (floor->exact (/ n 2))))))) CROSSREFS Cf. A010051, A292597, A292598. Cf. also A292599 (variant for all primes). Sequence in context: A151867 A262563 A170843 * A011023 A284610 A234017 Adjacent sequences:  A292593 A292594 A292595 * A292597 A292598 A292599 KEYWORD nonn AUTHOR Antti Karttunen, Sep 27 2017 STATUS approved

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Last modified February 19 04:00 EST 2020. Contains 332034 sequences. (Running on oeis4.)