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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).
1
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?
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jan 30 2003
EXTENSIONS
Typo in data corrected by Sean A. Irvine, Aug 22 2025
STATUS
approved