A270834 -id:A270834

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A270951

Numbers k such that k | A000129(k-1).

+10
3

1, 7, 17, 23, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 169, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 311, 313, 337, 353, 359, 367, 383, 385, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 599, 601, 607, 617, 631, 641, 647, 673, 719, 727, 743

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OFFSET

1,2

COMMENTS

Although A246692 and this sequence have similar names, note that this sequence generates prime numbers most of the time.

Composite terms of this sequence are A351337.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

7 is a term because A000129(6) = 70 is divisible by 7.

MATHEMATICA

Select[Range[1000], Divisible[Fibonacci[#-1, 2], #]&] (* Jean-François Alcover, Jun 06 2017 *)

PROG

(PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];

for(n=1, 1e3, if(Mod(a000129(n-1), n) == 0, print1(n, ", ")));

(PARI) is(n)=(Mod([2, 1; 1, 0], n)^(n-1))[2, 1]==0 \\ Charles R Greathouse IV, Sep 11 2022

CROSSREFS

Cf. A000129, A001132, A246692, A270834, A351337 (composite terms).

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Mar 26 2016

STATUS

approved

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