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
Examples
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; ...
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.
Programs
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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
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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 *) -
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)), ", "));
Comments