A078349 Number of primes in sequence h(m) defined by h(1) = n, h(m+1) = Floor(h(m)/2).

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, 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, 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

Offset: 1

Author

Joseph L. Pe, Dec 23 2002

Keywords

• nonn

Examples

			The sequence h(m) for n = 5 is 5, 2, 1, 0, 0, 0, ...., in which two terms are primes. Therefore a(5) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A010051, A292258, A292259, A292598, A292599, A292936.

Programs

Mathematica

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}]

PARI

A078349(n) = if(1==n,0,isprime(n)+A078349(n\2)); \\ Antti Karttunen, Oct 01 2017

Formula

From Antti Karttunen, Oct 01 2017: (Start)

a(1) = 0; for n > 1, a(n) = A010051(n) + a(floor(n/2)).

a(n) = A000120(A292599(n)).

a(n) = A007814(A292258(n)).

a(n) >= A292598(n).

a(n) >= A292936(n).

(End)