A088340 Numbers k such that frac(x^k) = frac(x*frac(x^(k-1))) where x=5/2 and frac(x) denotes the fractional part of x.

0, 2, 3, 7, 8, 10, 11, 13, 16, 17, 18, 20, 21, 23, 25, 27, 29, 31, 34, 35, 36, 39, 40, 41, 44, 46, 48, 49, 50, 52, 53, 59, 60, 62, 63, 69, 70, 71, 72, 76, 77, 78, 79, 82, 84, 86, 88, 89, 90, 92, 93, 99, 100, 101, 104, 105, 107, 108, 110, 111, 114, 115, 116, 118, 124, 125

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) appears to be asymptotic to 2*n and a(n)=2n for infinitely many values of n such as n=82, 89, 130, 138, 600, 604, 645, ... - Corrected by Robert Israel, Jan 20 2022

Maple

filter:= n -> frac((5/2)^n) = frac(5/2*frac((5/2)^(n-1))):select(filter, [$0..1000]); # Robert Israel, Jan 20 2022

Crossrefs

Sequence in context: A129341 A115985 A131210 * A288696 A163517 A047532

Adjacent sequences: A088337 A088338 A088339 * A088341 A088342 A088343

Keyword

nonn

Author

Benoit Cloitre, Nov 07 2003

Status

approved