A113194 Numbers k such that Lucas(k) - Lucas(i) is composite for i=0..k-3.

5, 7, 10, 17, 19, 23, 29, 31, 34, 41, 44, 49, 53, 55, 57, 62, 67, 68, 71, 75, 77, 79, 80, 87, 89, 93, 98, 100, 101, 103, 107, 109, 110, 116, 122, 124, 125, 133, 134, 135, 136, 143, 147, 154, 155, 160, 161, 164, 167, 170, 173, 177, 180, 184, 185, 188, 190, 194, 196

Offset

1,1

Comments

These are the numbers k such that A113193(k) = 0.

Links

Robert Israel, Table of n, a(n) for n = 1..2600

Maple

Luc:= 2, 1, 3: R:= NULL: count:= 0:
a:= 1: b:= 3:
for n from 3 while count < 100 do
  c:= a+b; a:= b; b:=c; Luc:= Luc, c;
  if ormap(isprime, [seq(c-Luc[i], i=1..n-2)]) then next fi;
  R:= R, n; count:= count+1;
od:
R; # Robert Israel, Jan 18 2023

Mathematica

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

Crossrefs

Cf. A000032, A113192 (primes that are the difference of two Lucas numbers).

Cf. A113193.

Sequence in context: A073895 A356701 A320447 * A356103 A339211 A088768

Adjacent sequences: A113191 A113192 A113193 * A113195 A113196 A113197

Keyword

nonn

Author

T. D. Noe, Oct 17 2005

Status

approved