

A207790


Permutation of positive numbers. See comments.


4



1, 2, 4, 3, 8, 5, 6, 7, 16, 11, 9, 13, 12, 17, 10, 19, 32, 23, 14, 29, 18, 31, 15, 37, 24, 41, 21, 43, 20, 47, 22, 53, 64, 59, 25, 61, 27, 67, 26, 71, 36, 73, 33, 79, 28, 83, 34, 89, 48, 97, 35, 101, 30, 103, 38, 107, 40, 109, 39, 113, 42, 127, 46, 131, 128, 137, 49, 139, 44, 149, 51, 151
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OFFSET

1,2


COMMENTS

a(1)=1; on places 2,4,6,8,... we put primes (A000040); on places 3,7,11,15,... we put products of two primes (A001358); on places 5,13,21,29,... we put products of three primes (A014612); on places 9,25,41,57,... we put products of four primes (A014613); on places 17,49,81,... we put products of five primes (A014614); etc.
Primes with the index not exceeding n have density 1/2, semiprimes have density 1/4, etc.
By our system, here and in A207800, A207801, A207802 we used the order: a(1)=1; the first appearance of a new kind of numbers in places of the form 2^k+1, k=0,1,2,..., with period of the appearance 2^{k+1}.


LINKS



FORMULA



MATHEMATICA

mx = 72; a = Array[1 &, mx]; cnt = mx  1; offs = Table[2^(i  1) + 1, {i, 1, mx}]; n = 1; While[cnt > 0, n++; idx = PrimeOmega[n]; pos = offs[[idx]]; If[pos > mx, Continue[]]; offs[[idx]] += 2^idx; a[[pos]] = n; cnt]; a (* Ivan Neretin, May 06 2015 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



