A261091 a(n) = number of steps required to reach F(n+1)-1 from F(n+2)-1 by repeatedly subtracting from a natural number the number of ones in its Zeckendorf representation. Here F(n) = the n-th Fibonacci number, F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, ...

0, 1, 1, 1, 2, 2, 3, 5, 8, 11, 17, 25, 37, 56, 85, 130, 199, 305, 469, 723, 1118, 1733, 2693, 4193, 6539, 10211, 15962, 24974, 39103, 61262, 96030, 150608, 236338, 371101, 583118, 916978, 1443204, 2273434, 3584522, 5656786, 8934696, 14123156, 22340250

Offset

0,5

Links

Table of n, a(n) for n=0..42.

Formula

a(n) = A219642(A000071(n+2)) - A219642(A000071(n+1)). [By definition.]

a(n) = A219642(A000045(n+2)) - A219642(A000045(n+1)). [Equally.]

Prog

(Scheme) (define (A261091 n) (let ((end (- (A000045 (+ 1 n)) 1))) (let loop ((k (- (A000045 (+ 2 n)) 1)) (s 0)) (if (= k end) s (loop (A219641 k) (+ 1 s))))))

Crossrefs

Cf. A000045, A000071, A219641, A219642.

From a(1) onward the first differences of both A261081 and A261082.

Cf. A261090 (first differences of this sequence).

Cf. also A261102, A261076.

Sequence in context: A076777 A240210 A111123 * A179523 A087729 A039890

Adjacent sequences: A261088 A261089 A261090 * A261092 A261093 A261094

Keyword

nonn

Author

Antti Karttunen, Aug 08 2015

Status

approved