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

Author

Antti Karttunen, Aug 08 2015

Keywords

• nonn

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.

Programs

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))))))

Formula

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

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