A257808 - OEIS

%I #12 May 13 2015 15:44:18

%S 0,0,1,2,2,3,4,4,5,5,6,7,7,8,9,10,11,11,11,12,13,13,14,14,14,14,15,15,

%T 16,17,17,18,19,20,20,20,21,22,22,23,24,24,24,25,26,27,28,29,30,30,31,

%U 32,32,32,32,32,33,33,34,35,35,36,37,38,38,38,39,40,40,41,41,42,43,43,43,43,43,43,44,45,46,46,46,46,47,48,49,50,51

%N a(n) = number of nonzero even numbers in range 0 .. n of A233271, the infinite trunk of inverted binary beanstalk.

%C a(n) = the largest number k such that A257804(k) <= n.

%H Antti Karttunen, <a href="/A257808/b257808.txt">Table of n, a(n) for n = 0..16405</a>

%F a(0) = 0; for n >= 1, a(n) = (1-A257800(n)) + a(n-1).

%F Other identities. For all n >= 0:

%F a(n) = A257806(n) + A257807(n).

%F a(A257804(n)) = n. [This sequence works as a left inverse for injection A257804.]

%o (Scheme, with memoization-macro definec)

%o (definec (A257808 n) (if (zero? n) n (+ (- 1 (A257800 n)) (A257808 (- n 1)))))

%Y Cf. A233271, A257800, A257804, A257806, A257807.

%K nonn

%O 0,4

%A _Antti Karttunen_, May 12 2015