

A228440


Numbers n dividing u(n), where the Lucas sequence is defined u(i) = u(i1)  3*u(i2) with initial conditions u(0)=0, u(1)=1.


1



1, 11, 121, 253, 1331, 2783, 5819, 11891, 14641, 29161, 30613, 64009, 130801, 133837, 161051, 273493, 320771, 336743, 558877, 640343, 670703, 704099, 895873, 1438811, 1472207, 1771561, 3008423, 3078251, 3528481, 3544453, 3704173, 6147647, 6290339, 7027801
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OFFSET

1,2


COMMENTS

Since the absolute value of the discriminant of the characteristic polynomial is prime (=11), the sequence contains every nonnegative integer power of 11 (A001020 is subsequence). Other terms are formed on multiplication of 11^k by sporadic primes.


LINKS

Lars Blomberg, Table of n, a(n) for n = 1..65
C. Smyth, The Terms in Lucas Sequences Divisible by their Indices, Journal of Integer Sequences, Vol.13 (2010), Article 10.2.4
Wikipedia, Lucas sequence


EXAMPLE

u(1)=1 and u(11)=253. Clearly n divides u(n) for these terms.


MATHEMATICA

nn = 10000; s = LinearRecurrence[{1, 3}, {1, 1}, nn]; t = {}; Do[
If[Mod[s[[n]], n] == 0, AppendTo[t, n]], {n, nn}]; t (* T. D. Noe, Nov 06 2013 *)


CROSSREFS

Cf. A214733 (Lucas sequence u(n) ignoring sign).
Cf. A001020 (powers of 11).
Sequence in context: A084969 A045592 A045595 * A015958 A014951 A223223
Adjacent sequences: A228437 A228438 A228439 * A228441 A228442 A228443


KEYWORD

nonn


AUTHOR

Thomas M. Bridge, Nov 02 2013


EXTENSIONS

a(27)a(34) from Lars Blomberg, Feb 15 2016


STATUS

approved



