A099564 a(0) = 0; for n > 0, a(n) = final nonzero number in the sequence n, f(n,2), f(f(n,2),3), f(f(f(n,2),3),4),..., where f(n,d)=Floor(n/F(d+1)), with F denoting the Fibonacci numbers (A000045).

0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 0

Author

John W. Layman, Oct 22 2004

Keywords

• nonn

Comments

Records in {a(n)} are given in A099565.

a(n) gives the most significant digit of n when written in "base A003266", like A099563 and A276153 give the most significant digit in bases A000142 and A002110 respectively. - Antti Karttunen, Aug 23 2016

Links

• Antti Karttunen, Table of n, a(n) for n = 0..3120

Crossrefs

Cf. A000045, A003266, A099565 (positions of records).

Differs from A099563 for the first time at n=24.

Differs from A276153 for the first time at n=210, where a(210)=7, while A276153(210)=1.

Programs

Scheme

(define (A099564 n) (let loop ((n n) (i 3)) (let* ((f (A000045 i)) (dig (modulo n f)) (next-n (/ (- n dig) f))) (if (zero? next-n) dig (loop next-n (+ 1 i))))))
;; Standalone version:
(define (A099564 n) (let loop ((n n) (f1 1) (f2 2)) (let* ((dig (modulo n f2)) (next-n (/ (- n dig) f2))) (if (zero? next-n) dig (loop next-n f2 (+ f1 f2))))))
;; Antti Karttunen, Aug 23 2016

Extensions

a(0) = 0 prepended and the name corrected by Antti Karttunen, Aug 23 2016