A289772 a(n) is the numerator of b(n) where b(n) = 1/(3*(1+2*A112765(n) - b(n-1))) and b(0) = 0, where A112765(n) is the 5-adic valuation of n.

0, 1, 1, 2, 1, 1, 2, 5, 3, 4, 1, 5, 4, 7, 3, 2, 3, 7, 4, 5, 1, 4, 3, 5, 2, 1, 3, 8, 5, 7, 2, 11, 9, 16, 7, 5, 8, 19, 11, 14, 3, 13, 10, 17, 7, 4, 5, 11, 6, 7, 1, 8, 7, 13, 6, 5, 9, 22, 13, 17, 4, 19, 15, 26, 11, 7, 10, 23, 13, 16, 3, 11, 8, 13, 5, 2, 5, 13, 8, 11, 3

Offset

0,4

Comments

For n>0, a(n)/A289773(n) lists the rationals of a quinary analog of the Calkin-Wilf tree. See the Ponton link.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Lionel Ponton, Two trees enumerating the positive rationals, arXiv:1707.02366 [math.NT], 2017. See p. 7.

Lionel Ponton, Two trees enumerating the positive rationals, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A17.

Example

Tree of rationals begin:
0;
1/3;
1/2, 2/3, 1, 1/6, 2/5;
5/9, 3/4, 4/3, 1/5, 5/12, 4/7, 7/9, 3/2, 2/9, 3/7, 7/12, 4/5, 5/3, 1/4, 4/9, 3/5, 5/6, 2, 1/9, 3/8, 8/15, 5/7, 7/6, 2/11, 11/27;
...

Maple

b:= proc(n) option remember; 1/(3*(1+2*padic:-ordp(n, 5)-procname(n-1))) end proc:
b(0):= 0:
map(numer@b, [$0..100]); # Robert Israel, Jul 12 2017

Mathematica

a[0] = 0; a[n_] := a[n] = 1/(3 (1 + 2 IntegerExponent[n, 5] - a[n - 1])); Table[Numerator@ a@ n, {n, 0, 80}] (* Michael De Vlieger, Jul 12 2017 *)

Prog

(PARI) b(n) = if (n==0, 0, 1/(3*(1+2*valuation(n, 5) - b(n-1))));
lista(nn) = for (n=0, nn, print1(numerator(b(n)), ", "));

Crossrefs

Cf. A002487, A277749, A277750, A289773.

Sequence in context: A159046 A029937 A368926 * A283615 A172483 A216396

Adjacent sequences: A289769 A289770 A289771 * A289773 A289774 A289775

Keyword

nonn,frac,tabf,look

Author

Michel Marcus, Jul 12 2017

Status

approved