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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 (list; graph; refs; listen; history; text; internal format)
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

Ivan Neretin, Table of n, a(n) for n = 1..8192

FORMULA

For n>1, a(n) = A078840(A249725(n-1)). - Ivan Neretin, Apr 30 2016

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

Cf. A057114.

Sequence in context: A329146 A246367 A048167 * A305427 A269375 A135141

Adjacent sequences:  A207787 A207788 A207789 * A207791 A207792 A207793

KEYWORD

nonn

AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Feb 20 2012

STATUS

approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)