A214897 -id:A214897 - cp's OEIS frontend

A214898 Conway's subprime Fibonacci sequence, largest loop elements.

2, 827, 607, 239, 191, 5693, 347

Offset: 1

Wouter Meeussen, Jul 29 2012

nonn

Similar to the Fibonacci recursion starting with a pair of positive integers, but each new nonprime term is divided by its least prime factor. Recursion enters a loop of length A214897(n), of which the largest element a(n) is prime (this sequence).

Richard K. Guy, Tanya Khovanova and Julian Salazar, Conway's subprime Fibonacci sequences, arXiv:1207.5099v1 [math.NT]

Cf. A000045, A020639, A175723, A214551, A014682, A214674, A214892-A214898.

Mathematica
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see A214674
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A282814 Table read by antidiagonals (n > 0, k > 0): T(n, k) is the length of the loop in Conway's subprime Fibonacci sequence with starting values of n and k.

Original entry on oeis.org

18, 18, 18, 18, 1, 18, 136, 18, 18, 136, 18, 18, 1, 18, 136, 18, 18, 18, 136, 18, 18, 136, 18, 136, 1, 18, 136, 18, 18, 18, 1, 18, 136, 1, 18, 18, 136, 18, 18, 136, 1, 18, 18, 136, 18, 18, 18, 18, 18, 18, 18, 136, 136, 136, 18, 18, 136, 1, 18, 18, 1, 18, 18

Offset: 1

Peter Kagey, Feb 21 2017

All terms are in A214897, which is conjectured to be finite. - Peter Kagey, Nov 04 2017

			T(1, 1) = 18 because 18 is the loop length in Conway's subprime Fibonacci sequence when starting with 1, 1 (A214674). (i.e., A214674(n) = A214674(n + 18) for n >= 38 = A282813(1, 1).)
Upper-left corner of table:
   18  18  18 136 136  18  18  18  18  18 ...
   18   1  18  18  18 136  18 136 136  18 ...
   18  18   1 136  18   1  18 136  18  18 ...
  136  18  18   1 136  18 136  18  18 136 ...
   18  18 136  18   1  18  18  18 136   1 ...
   18  18   1 136  18   1  18  18  18  18 ...
  136  18  18  18  18  18   1 136  18  18 ...
   18  18  18  18 136  18  18   1  18  18 ...
  136  18   1  18  18  18 136  18   1 136 ...
   18 136  18 136   1  18 136  18  18   1 ...
  ...

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A214674, A214897, A282813, A282814.

cp's OEIS Frontend

A214898 Conway's subprime Fibonacci sequence, largest loop elements.

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