A113194 - OEIS

%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