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A337172
Numbers k such that L(k+2)^L(k) mod L(k+1) is a Lucas number, where L = A000032.
0
1, 2, 3, 6, 11, 14
OFFSET
1,2
COMMENTS
No other terms < 5000.
EXAMPLE
L(3) ^ L(1) mod L(2) = 4^1 mod 3 = 1 = L(1).
L(4) ^ L(2) mod L(3) = 7^3 mod 4 = 3 = L(2).
L(5) ^ L(3) mod L(4) = 11^4 mod 7 = 4 = L(3).
L(8) ^ L(6) mod L(7) = 47^18 mod 29 = 4 = L(3).
L(13) ^ L(11) mod L(12) = 521^199 mod 322 = 199 = L(11).
L(16) ^ L(14) mod L(15) = 2207^843 mod 1364 = 123 = L(10).
MAPLE
luc:= n -> 2*combinat:-fibonacci(n-1) + combinat:-fibonacci(n):
isluc:= proc(n) local m, phi; phi:= (1+sqrt(5))/2;
m:= round(log[phi](n));
n = luc(m);
end proc:
isluc(1):= true: isluc(2):= true:
select(n -> isluc(luc(n+2) &^ luc(n) mod luc(n+1)), [$1..1000]);
CROSSREFS
Cf. A000032.
Sequence in context: A057758 A057125 A018687 * A361103 A294510 A218155
KEYWORD
nonn,bref,more
AUTHOR
J. M. Bergot and Robert Israel, Jan 28 2021
STATUS
approved