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%I #12 Jan 19 2023 11:10:06
%S 5,7,10,17,19,23,29,31,34,41,44,49,53,55,57,62,67,68,71,75,77,79,80,
%T 87,89,93,98,100,101,103,107,109,110,116,122,124,125,133,134,135,136,
%U 143,147,154,155,160,161,164,167,170,173,177,180,184,185,188,190,194,196
%N Numbers k such that Lucas(k) - Lucas(i) is composite for i=0..k-3.
%C These are the numbers k such that A113193(k) = 0.
%H Robert Israel, <a href="/A113194/b113194.txt">Table of n, a(n) for n = 1..2600</a>
%p Luc:= 2,1,3: R:= NULL: count:= 0:
%p a:= 1: b:= 3:
%p for n from 3 while count < 100 do
%p c:= a+b; a:= b; b:=c; Luc:= Luc,c;
%p if ormap(isprime, [seq(c-Luc[i],i=1..n-2)]) then next fi;
%p R:= R, n; count:= count+1;
%p od:
%p R; # _Robert Israel_, Jan 18 2023
%t lst={}; Do[i=0; While[i<n-2 && !PrimeQ[Lucas[n]-Lucas[i]], i++ ]; If[i==n-2, AppendTo[lst, n]], {n, 3, 250}]; lst
%Y Cf. A000032, A113192 (primes that are the difference of two Lucas numbers).
%Y Cf. A113193.
%K nonn
%O 1,1
%A _T. D. Noe_, Oct 17 2005
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