A289773 a(n) is the denominator of b(n) where b(n) = 1/(3*(1+2*A112765(n) - b(n-1))) and b(0) = 0, with A112765(n) being the 5-adic valuation of n.

1, 3, 2, 3, 1, 6, 5, 9, 4, 3, 5, 12, 7, 9, 2, 9, 7, 12, 5, 3, 4, 9, 5, 6, 1, 9, 8, 15, 7, 6, 11, 27, 16, 21, 5, 24, 19, 33, 14, 9, 13, 30, 17, 21, 4, 15, 11, 18, 7, 3, 8, 21, 13, 18, 5, 27, 22, 39, 17, 12, 19, 45, 26, 33, 7, 30, 23, 39, 16, 9, 11, 24, 13, 15, 2, 15, 13

Offset

0,2

Comments

For n>0, A289772(n)/a(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(denom@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[Denominator@ a@ n, {n, 0, 76}] (* 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(denominator(b(n)), ", "));

Crossrefs

Cf. A002487, A277749, A277750, A289772.

Sequence in context: A070032 A204915 A165026 * A197475 A195381 A144558

Adjacent sequences: A289770 A289771 A289772 * A289774 A289775 A289776

Keyword

nonn,frac,tabf,look

Author

Michel Marcus, Jul 12 2017

Status

approved