A207801 -id:A207801 - cp's OEIS frontend

A207790 Permutation of positive numbers. See comments.

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

Offset: 1

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

nonn

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}.

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

Cf. A057114.

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 *)

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

A207802 Permutation of positive numbers. See comments.

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 6, 16, 7, 32, 9, 64, 10, 128, 12, 256, 11, 512, 18, 1024, 15, 2048, 24, 4096, 14, 8192, 27, 16384, 20, 32768, 36, 65536, 13, 131072, 48, 262144, 25, 524288, 54, 1048576, 21, 2097152, 72, 4194304, 30, 8388608, 81, 16777216, 22, 33554432, 96, 67108864, 40, 134217728, 108

Offset: 1

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

nonn

a(1)=1; on places 2,4,6,8,... we put 2^m, m=1,2,3,..., i.e., numbers with the greatest prime divisor p_1=2; on places 3,7,11,15,... we put numbers with the greatest prime divisor p_2=3; on places 5,13,21,29,... we put numbers with the greatest prime divisor p_3=5; etc.

For general description of the order, see the comment in A207790.

Cf. A207790, A207800, A207801.

For n>1, a(n) = A125624(A209268(n-1)). - Ivan Neretin, Apr 30 2016

a(30) fixed by Ivan Neretin, Apr 30 2016

cp's OEIS Frontend

A207790 Permutation of positive numbers. See comments.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula