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%I #46 Apr 01 2023 11:24:55
%S 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,
%T 27,28,25,26,34,32,31,33,36,37,35,39,38,42,40,46,41,45,44,43,47,53,51,
%U 50,52,49,61,48,54,58,55,60,59,56,57,62,66,65,64,63,67,68,71,70
%N Numerators of fractions n/prime(n) sorted in decreasing order.
%C 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.
%H Petr Platais, <a href="/A350778/b350778.txt">Table of n, a(n) for n = 1..10000</a>
%H Petr Platais, <a href="/A350778/a350778_1.png">Scatterplot of cumulative sums of signs of first differences</a>
%H Rémy Sigrist, <a href="/A350778/a350778.png">Scatterplot of the first differences of the first 100000 terms</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%t Take[Numerator[ReverseSort[Table[n/Prime[n], {n, 1, 100+10}]]], 100]
%o (Python)
%o from fractions import Fraction
%o from sympy import prime, primerange
%o def aupton(N, m=3): # m is safety factor
%o f = (Fraction(i, p) for i, p in enumerate(primerange(2, prime(m*N)), 1))
%o return [fn.numerator for fn in sorted(f, reverse=True)][:N]
%o print(aupton(100)) # _Michael S. Branicky_, Jan 15 2022
%o (PARI) lista(nn) = Vec(apply(numerator, vecsort(vector(3*nn, n, n/prime(n)), , 4)), nn); \\ _Michel Marcus_, Jan 17 2022
%K nonn,easy,frac
%O 1,1
%A _Petr Platais_, Jan 15 2022