A207801 Permutation of positive numbers. See comments.

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 25, 14, 21, 16, 11, 18, 27, 20, 35, 22, 33, 24, 49, 26, 39, 28, 55, 30, 45, 32, 13, 34, 51, 36, 65, 38, 57, 40, 77, 42, 63, 44, 85, 46, 69, 48, 121, 50, 75, 52, 95, 54, 81, 56, 91, 58, 87, 60, 115, 62, 93, 64, 17, 66, 99, 68, 125, 70, 105, 72, 119, 74

Offset: 1

Author

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

Keywords

• nonn

Comments

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

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

Links

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

Crossrefs

Cf. A207790, A207800.

Programs

Mathematica

a = Array[1 &, mx = 74]; cnt = mx - 1; offs = Table[2^(i - 1) + 1, {i, 1, mx}]; n = 1; While[cnt > 0, n++; idx = PrimePi[FactorInteger[n][[1, 1]]]; pos = offs[[idx]]; If[pos > mx, Continue[]]; offs[[idx]] += 2^idx; a[[pos]] = n; cnt--]; a (* Ivan Neretin, May 06 2015 *)

Formula

For n>1, a(n) = A083140(1+A209268(n-1)). Equivalently, a(n) = A083221(1+A249725(n-1)). - Ivan Neretin, Apr 30 2016