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%I #10 Mar 26 2020 11:13:21
%S 0,1,1,1,2,1,2,1,1,2,3,1,2,2,2,1,2,1,2,2,2,3,4,1,1,2,2,2,3,2,3,1,1,2,
%T 2,1,2,2,2,2,3,2,3,3,3,4,5,1,1,1,1,2,3,2,2,2,2,3,4,2,3,3,3,1,1,1,2,2,
%U 2,2,3,1,2,2,2,2,2,2,3,2,2,3,4,2,2,3,3,3,4,3,3,4,4,5,5,1,2,1,1,1
%N Number of primes in sequence h(m) defined by h(1) = n, h(m+1) = Floor(h(m)/2).
%H Antti Karttunen, <a href="/A078349/b078349.txt">Table of n, a(n) for n = 1..16384</a>
%F From _Antti Karttunen_, Oct 01 2017: (Start)
%F a(1) = 0; for n > 1, a(n) = A010051(n) + a(floor(n/2)).
%F a(n) = A000120(A292599(n)).
%F a(n) = A007814(A292258(n)).
%F a(n) >= A292598(n).
%F a(n) >= A292936(n).
%F (End)
%e The sequence h(m) for n = 5 is 5, 2, 1, 0, 0, 0, ...., in which two terms are primes. Therefore a(5) = 2.
%t f[n_] := Module[{i, p}, i = n; p = 0; While[i > 1, If[PrimeQ[i], p = p + 1]; i = Floor[i/2]]; p]; Table[f[i], {i, 1, 100}]
%o (MIT/GNU Scheme, with memoization-macro definec)
%o (definec (A078349 n) (if (<= n 1) 0 (+ (A010051 n) (A078349 (floor->exact (/ n 2)))))) ;; _Antti Karttunen_, Oct 01 2017
%o (PARI) A078349(n) = if(1==n,0,isprime(n)+A078349(n\2)); \\ _Antti Karttunen_, Oct 01 2017
%Y Cf. A010051, A292258, A292259, A292598, A292599, A292936.
%K nonn
%O 1,5
%A _Joseph L. Pe_, Dec 23 2002
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