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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).
6
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
0,5
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
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
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