The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A128332

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A128332

a(0)=a(1)=1. For n >= 2, a(n) = number of positive numbers <= n that are coprime to a(n-1) + a(n-2).
(history; published version)

#17 by Joerg Arndt at Tue Feb 12 01:16:00 EST 2019

STATUS

proposed

approved

#16 by Michel Marcus at Tue Feb 12 00:21:39 EST 2019

STATUS

editing

proposed

#15 by Michel Marcus at Tue Feb 12 00:21:30 EST 2019

CROSSREFS

Cf. A000010 (number of positive numbers <= n that are coprime to n).

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proposed

editing

Discussion

Tue Feb 12

00:21

Michel Marcus: ok ?

#14 by Jon E. Schoenfield at Mon Feb 11 23:33:13 EST 2019

STATUS

editing

proposed

#13 by Jon E. Schoenfield at Mon Feb 11 23:33:10 EST 2019

NAME

a(0)=a(1)=1. For n >= 2, a(n) = number of positive numbers <= n that are coprime to a(n-1) + a(n-2).

EXAMPLE

a(5) + a(6) = 10. The number of positive integers <= 7 that are coprime to 10 is three, these integers being 1, 3 and 7. So a(7) = 3.

MAPLE

a[0]:=1: a[1]:=1: for n from 2 to 100 do ct:=0: for j from 1 to n do if igcd(j, a[n-1]+a[n-2])=1 then ct:=ct+1 else fi od: a[n]:=ct: od: seq(a[n], n=0..100); - _# _Emeric Deutsch_, May 07 2007

STATUS

approved

editing

#12 by Joerg Arndt at Thu Jun 02 05:39:20 EDT 2016

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proposed

approved

#11 by Ivan Neretin at Thu Jun 02 05:25:07 EDT 2016

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editing

proposed

#10 by Ivan Neretin at Thu Jun 02 05:25:03 EDT 2016

LINKS

Ivan Neretin, <a href="/A128332/b128332.txt">Table of n, a(n) for n = 0..10000</a>

STATUS

approved

editing

#9 by Harvey P. Dale at Wed Jan 21 11:56:34 EST 2015

STATUS

editing

approved

#8 by Harvey P. Dale at Wed Jan 21 11:56:28 EST 2015

MATHEMATICA

nxt[{n_, a_, b_}]:={n+1, b, Count[Range[n+1], _?(CoprimeQ[a+b, #]&)]}; Transpose[ NestList[ nxt, {1, 1, 1}, 80]][[2]] (* Harvey P. Dale, Jan 21 2015 *)

STATUS

approved

editing