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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)