login
A078349
Number of primes in sequence h(m) defined by h(1) = n, h(m+1) = Floor(h(m)/2).
6
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
1,5
LINKS
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)
EXAMPLE
The sequence h(m) for n = 5 is 5, 2, 1, 0, 0, 0, ...., in which two terms are primes. Therefore a(5) = 2.
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}]
PROG
(MIT/GNU Scheme, with memoization-macro definec)
(definec (A078349 n) (if (<= n 1) 0 (+ (A010051 n) (A078349 (floor->exact (/ n 2)))))) ;; Antti Karttunen, Oct 01 2017
(PARI) A078349(n) = if(1==n, 0, isprime(n)+A078349(n\2)); \\ Antti Karttunen, Oct 01 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Dec 23 2002
STATUS
approved