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Integers that appear as ratios of Fibonacci numbers F(kn)/F(k), but omitting Fibonacci numbers F(n)/F(1) and Lucas numbers F(2n)/F(n).
3

%I #12 Oct 19 2017 03:13:45

%S 17,48,72,122,305,323,329,842,1292,1353,2208,2255,5473,5777,5796,

%T 15005,15128,15456,23184,24447,39602,98209,103683,103729,104005,

%U 105937,166408,271442,416020,439128,709805,710648,726103,1762289

%N Integers that appear as ratios of Fibonacci numbers F(kn)/F(k), but omitting Fibonacci numbers F(n)/F(1) and Lucas numbers F(2n)/F(n).

%H T. D. Noe, <a href="/A031122/b031122.txt">Table of n, a(n) for n=1..1000</a>

%o (PARI) a031122(mk,mn,x) = local(v,vv,j,i); v=[]; for(k=3,mk, for(n=3,mn,v=concat(v,[fibonacci(k*n)/fibonacci(k)]))); v=vecsort(v); vv=[v[1]]; for(j=2,matsize(v)[2], if(v[j-1]<v[j]&&v[j]<x,vv=concat(vv,[v[j]]))); i=1; vv; a031122(150,50,610000000) \\ _Klaus Brockhaus_, Oct 20 2001

%Y Cf. A031121.

%K nonn,easy

%O 1,1

%A _Dan Hoey_

%E Corrected and extended by _Don Reble_, Oct 20 2001