A099564 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

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

PROG

(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

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.

Sequence in context: A118164 A337198 A099563 * A341356 A276153 A341348

Adjacent sequences: A099561 A099562 A099563 * A099565 A099566 A099567

KEYWORD

nonn

AUTHOR

John W. Layman, Oct 22 2004

EXTENSIONS

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

STATUS

approved