cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A023162 Numbers k such that F(k) == -1 (mod k), where F(n) = A000045(n) is the n-th Fibonacci number.

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%I A023162 #25 Nov 21 2018 02:31:40
%S A023162 1,2,3,4,7,13,14,17,23,26,34,37,43,46,47,53,67,73,74,83,86,94,97,103,
%T A023162 106,107,113,127,134,137,146,157,163,166,167,173,193,194,197,206,214,
%U A023162 223,226,227,233,254,257,263,274,277,283,293,307,313,314,317,326,334
%N A023162 Numbers k such that F(k) == -1 (mod k), where F(n) = A000045(n) is the n-th Fibonacci number.
%C A023162 If k is prime then k is in the sequence if and only if k == 2 or 3 (mod 5).
%H A023162 Alois P. Heinz, <a href="/A023162/b023162.txt">Table of n, a(n) for n = 1..10000</a>
%F A023162 a(n) seems to be asymptotic to c*n*log(n) where c = 1.5... - _Benoit Cloitre_, Jan 10 2003
%t A023162 Module[{nn = 500, fib}, fib = Thread[{Range[nn], Fibonacci[Range[nn]]}]; Transpose[Select[fib, Mod[Last[#], First[#]] == First[#] - 1 &]][[1]]] (* _Harvey P. Dale_, May 21 2014 *)
%t A023162 Select[Range[500], Mod[Fibonacci[#], #] == # - 1 &] (* _Alonso del Arte_, Nov 20 2018 *)
%o A023162 (PARI) isok(k) = Mod(fibonacci(k), k) == -1; \\ _Michel Marcus_, Nov 21 2018
%K A023162 nonn
%O A023162 1,2
%A A023162 _David W. Wilson_
%E A023162 Name clarified by _Alonso del Arte_ and _Michel Marcus_, Nov 20 2018