A205113 Least k such that n divides the k-th difference between distinct Lucas numbers.

1, 1, 2, 5, 7, 4, 9, 8, 20, 7, 14, 26, 17, 13, 12, 41, 11, 20, 44, 25, 42, 19, 22, 31, 18, 17, 113, 16, 27, 38, 119, 49, 46, 52, 42, 26, 68, 44, 48, 25, 54, 80, 24, 23, 59, 22, 35, 49, 47, 109, 71, 67, 58, 113, 63, 41, 132, 34, 87, 38

Offset: 1

Author

Clark Kimberling, Jan 22 2012

Keywords

• nonn
• look

Comments

The pairs of Lucas numbers are ordered as at A205112. For a guide to related sequences, see A204892.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A205114, A204892.

Programs

Maple

N:= 100: # to get terms before the first term > N*(N-1)/2
L:= proc(n) option remember; combinat:-fibonacci(n+1)+combinat:-fibonacci(n-1); end proc:
A205112:= [seq(seq(L(j)-L(i),i=1..j-1),j=2..N)]:
M:= N*(N-1)/2:
f:= proc(n) local k;
  for k from 1 to M do if A205112[k] mod n = 0 then return k fi od;
  -1
end proc:
R:= NULL:
for n from 1 do
v:= f(n);
if v = -1 then break fi;
R:= R,v
od:
R; # Robert Israel, Feb 25 2024

Mathematica

(See the program at A205114.)