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

1,3

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

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.)

Crossrefs

Cf. A205114, A204892.

Sequence in context: A200112 A146098 A296567 * A349047 A098486 A138320

Adjacent sequences: A205110 A205111 A205112 * A205114 A205115 A205116

Keyword

nonn,look

Author

Clark Kimberling, Jan 22 2012

Status

approved