A079626 Let u(1) = u(2) = 1, u(n) = abs(u(n-1) - 3/2*u(n-2)); then a(n) is the exponent of 2 in the denominator of u(n).

0, 0, 1, 0, 2, 2, 3, 0, 4, 4, 5, 4, 6, 6, 7, 4, 8, 8, 9, 8, 10, 10, 11, 10, 12, 12, 13, 9, 14, 14, 15, 14, 16, 16, 17, 16, 18, 18, 19, 17, 20, 20, 21, 19, 22, 22, 23, 21, 24, 24, 25, 23, 26, 26, 27, 26, 28, 28, 29, 27, 30, 30, 31, 30, 32, 32, 33, 31, 34, 34, 35, 34, 36, 36, 37, 35

Offset

1,5

Comments

Does u(n) diverge to infinity?

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) < n/2, a(2*n+1) = n.

Maple

u:= proc(n) u(n):= abs(u(n-1)-3/2*u(n-2)) end: u(1), u(2):=1$2:
a:= n-> padic[ordp](denom(u(n)), 2):
seq(a(n), n=1..76);  # Alois P. Heinz, Aug 22 2025

Mathematica

Module[{u, n}, IntegerExponent[Denominator[RecurrenceTable[{u[n] == Abs[u[n-1] - 3*u[n-2]/2], u[1] == u[2] == 1}, u, {n, 100}]], 2]] (* Paolo Xausa, Aug 25 2025 *)

Prog

(PARI) a=b=1; for(n=3, 100, c=abs(b-3*a/2); a=b; b=c; print1(valuation(denominator(c), 2), ", "))

Crossrefs

Sequence in context: A137345 A060755 A104594 * A257697 A088864 A330925

Adjacent sequences: A079623 A079624 A079625 * A079627 A079628 A079629

Keyword

nonn

Author

Benoit Cloitre, Jan 30 2003

Extensions

Typo in data corrected by Sean A. Irvine, Aug 22 2025

Status

approved