A099565 -id:A099565 - cp's OEIS frontend

A099566 A099565(n)/n.

1, 2, 6, 6, 30, 30, 30, 240, 240, 240, 240, 240, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 3120, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520, 65520

Offset: 1

John W. Layman, Oct 25 2004

nonn

Notice that the runs of equal terms of this sequence gives the Fibonacci sequence. Also, if all duplicate terms are deleted, the resulting sequence, {1,2,6,30,240,3120,...}, appears to be A003266, the product of first n nonzero Fibonacci numbers F(1), ..., F(n).

Cf. A099563, A099564, A099565.

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).

Original entry on oeis.org

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

John W. Layman, Oct 22 2004

nonn

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

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

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.

(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

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

cp's OEIS Frontend

A099566 A099565(n)/n.

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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).

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