

A289773


a(n) is the denominator of b(n) where b(n) = 1/(3*(1+2*A112765(n)  b(n1)) and b(0) = 0, with A112765(n) being the 5adic valuation of n.


2



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
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OFFSET

0,2


COMMENTS

For n>0, A289772(n)/a(n) lists the rationals of a quinary analog of the CalkinWilf 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(n1))) 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(n1))));
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



