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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A305313 A159046 A029937 * A283615 A216396 A273488

Adjacent sequences:  A289769 A289770 A289771 * A289773 A289774 A289775

KEYWORD

nonn,frac,tabf,look

AUTHOR

Michel Marcus, Jul 12 2017

STATUS

approved

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Last modified January 18 01:05 EST 2020. Contains 330995 sequences. (Running on oeis4.)