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A263161 Positive values of n such that A000071(n+2) is divisible by A000217(n). 2
1, 240, 600, 768, 1008, 1200, 1320, 1800, 2160, 2688, 2736, 3000, 3360, 3888, 4800, 5280, 5520, 6120, 6479, 6480, 6720, 6840, 7320, 7680, 8208, 8640, 9000, 9600, 9720, 10368, 11160, 11663, 12240, 12288, 13200, 13248, 13440, 13680, 14400, 15120, 15360, 15456, 16560, 18048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Interestingly, the minimum value of a(n) - a(n-1) is 1. Is there a maximum value of a(n) - a(n-1)?

From Robert Israel, Oct 19 2015: (Start)

n is in the sequence if either n is odd and A001175(n) and A001175((n+1)/2) both divide n+1, or n is even and A001175(n/2) and A001175(n+1) both divide n.

Most of the terms of the sequence appear to fall in these categories. The first two that do not are 15456 and 41640.

In particular, if n = 2^j * 3^k * 5^m with j >= 4, k >= 1 and m >= 1, and n+1 is prime, then n is in the sequence.  There are believed to be infinitely many numbers of this form.  The first few are 240, 1200, 2160, 4800, 6480, 7680, 8640, 9600, 14400, 15360. (End)

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

For n = 1, A000071(1+2) = 1 is divisible by A000217(1) = 1.

MAPLE

fmod:= proc(a, b) local A, t;

  uses LinearAlgebra[Modular];

  if b < 4295022903 then t:= integer[8] else t:= integer fi;

  A:= Mod(b, <<1, 1>|<1, 0>>, t);

  MatrixPower(b, A, a)[1, 2];

end proc:

filter:= n -> (fmod(n+2, n*(n+1)/2) = 1):

filter(1):= true:

select(filter, [$1..10^5]); # Robert Israel, Oct 19 2015

MATHEMATICA

fQ[n_] := Mod[Fibonacci[n + 2] - 1, n (n + 1)/2] == 0; Select[Range@20000, fQ] (* Bruno Berselli, Oct 19 2015 - after Robert G. Wilson v in A263225 *)

PROG

(PARI) for(n=1, 20000, if((fibonacci(n+2)-1) % (n*(n+1)/2) == 0, print1(n", ")));

(PARI) is(n)=((Mod([1, 1; 1, 0], n*(n+1)/2))^(n+2))[1, 2]==1 \\ Charles R Greathouse IV, Oct 19 2015

(MAGMA) [n: n in [1..20000] | IsDivisibleBy(Fibonacci(n+2)-1, n*(n+1) div 2)]; // Bruno Berselli, Oct 19 2015

CROSSREFS

Cf. A000045, A000071, A000217, A001175, A263225.

Sequence in context: A063372 A070123 A119659 * A268772 A202196 A060663

Adjacent sequences:  A263158 A263159 A263160 * A263162 A263163 A263164

KEYWORD

nonn

AUTHOR

Altug Alkan, Oct 11 2015

STATUS

approved

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Last modified May 16 21:29 EDT 2022. Contains 353720 sequences. (Running on oeis4.)