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 A292599 a(1) = 0; for n > 1, a(n) = A010051(n) + 2*a(floor(n/2)). 4
 0, 1, 1, 2, 3, 2, 3, 4, 4, 6, 7, 4, 5, 6, 6, 8, 9, 8, 9, 12, 12, 14, 15, 8, 8, 10, 10, 12, 13, 12, 13, 16, 16, 18, 18, 16, 17, 18, 18, 24, 25, 24, 25, 28, 28, 30, 31, 16, 16, 16, 16, 20, 21, 20, 20, 24, 24, 26, 27, 24, 25, 26, 26, 32, 32, 32, 33, 36, 36, 36, 37, 32, 33, 34, 34, 36, 36, 36, 37, 48, 48, 50, 51, 48, 48, 50, 50, 56, 57, 56, 56, 60, 60, 62, 62, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 1-bits in base-2 expansion of a(n) indicate the positions of 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) = 0; for n > 1, a(n) = A010051(n) + 2*a(floor(n/2)). Other identities. For all n >= 1: A000120(a(n)) = A078349(n). A007814(1+a(n)) = A292936(n). MAPLE A292599 := proc(n)     option remember;     if n = 1 then         0 ;     else         A010051(n) + 2*procname(floor(n/2)) ;     end if; end proc: seq(A292599(n), n=1..100) ; # R. J. Mathar, Sep 28 2017 MATHEMATICA a[1] = 0; a[n_] := a[n] = Boole[PrimeQ[n]] + 2*a[Floor[n/2]]; Array[a, 96] (* Jean-François Alcover, Sep 29 2017 *) PROG (Scheme, with memoization-macro definec) (definec (A292599 n) (if (<= n 1) 0 (+ (A010051 n) (* 2 (A292599 (floor->exact (/ n 2))))))) CROSSREFS Cf. A010051, A078349, A292258, A292259, A292936. Cf. also A292596 (variant for odd primes). Sequence in context: A173540 A336264 A070770 * A071487 A124071 A034697 Adjacent sequences:  A292596 A292597 A292598 * A292600 A292601 A292602 KEYWORD nonn AUTHOR Antti Karttunen, Sep 27 2017 STATUS approved

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Last modified December 4 15:14 EST 2021. Contains 349526 sequences. (Running on oeis4.)