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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

No other terms < 5000.

LINKS

Table of n, a(n) for n=1..6.

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 * A294510 A218155 A042944

Adjacent sequences:  A337169 A337170 A337171 * A337173 A337174 A337175

KEYWORD

nonn,bref,more

AUTHOR

J. M. Bergot and Robert Israel, Jan 28 2021

STATUS

approved

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Last modified May 7 02:20 EDT 2021. Contains 343636 sequences. (Running on oeis4.)