A350778 Numerators of fractions n/prime(n) sorted in decreasing order.

2, 3, 4, 1, 6, 5, 8, 7, 9, 11, 10, 14, 12, 15, 13, 16, 18, 17, 21, 19, 20, 22, 23, 24, 29, 30, 27, 28, 25, 26, 34, 32, 31, 33, 36, 37, 35, 39, 38, 42, 40, 46, 41, 45, 44, 43, 47, 53, 51, 50, 52, 49, 61, 48, 54, 58, 55, 60, 59, 56, 57, 62, 66, 65, 64, 63, 67, 68, 71, 70

Offset

1,1

Comments

A permutation of the positive integers. Computation of the first n terms of the sequence requires the generation and sorting of more than n fractions; exactly how many more is an open question.

Links

Petr Platais, Table of n, a(n) for n = 1..10000

Petr Platais, Scatterplot of cumulative sums of signs of first differences

Rémy Sigrist, Scatterplot of the first differences of the first 100000 terms

Index entries for sequences that are permutations of the natural numbers

Mathematica

Take[Numerator[ReverseSort[Table[n/Prime[n], {n, 1, 100+10}]]], 100]

Prog

(Python)
from fractions import Fraction
from sympy import prime, primerange
def aupton(N, m=3): # m is safety factor
    f = (Fraction(i, p) for i, p in enumerate(primerange(2, prime(m*N)), 1))
    return [fn.numerator for fn in sorted(f, reverse=True)][:N]
print(aupton(100)) # Michael S. Branicky, Jan 15 2022
(PARI) lista(nn) = Vec(apply(numerator, vecsort(vector(3*nn, n, n/prime(n)), , 4)), nn); \\ Michel Marcus, Jan 17 2022

Crossrefs

Sequence in context: A065338 A316272 A294649 * A001438 A342410 A345937

Adjacent sequences: A350775 A350776 A350777 * A350779 A350780 A350781

Keyword

nonn,easy,frac

Author

Petr Platais, Jan 15 2022

Status

approved