A123917 a(1)=1. a(n) = (the highest exponent in the prime-factorization of n)th integer from among those positive integers not occurring earlier in the sequence.

1, 2, 3, 5, 4, 6, 7, 10, 9, 8, 11, 13, 12, 14, 15, 19, 16, 18, 17, 21, 20, 22, 23, 26, 25, 24, 29, 28, 27, 30, 31, 36, 32, 33, 34, 37, 35, 38, 39, 42, 40, 41, 43, 45, 46, 44, 47, 51, 49, 50, 48, 53, 52, 56, 54, 58, 55, 57, 59, 61, 60, 62, 64, 69, 63, 65, 66, 68, 67, 70, 71, 74

Offset

1,2

Comments

This sequence is a permutation of the positive integers.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

12 has a prime-factorization of 2^2 *3^1 and the highest exponent is 2. So a(12) is the 2nd integer from among those positive integers not occurring among the first 11 terms of the sequence (i.e., the second integer from 12,13,14,...). So a(12) = 13.

Mathematica

f[l_List] := Block[{k = 0, c = Max @@ Last /@ FactorInteger[Length[l] + 1]}, While[c > 0, k++; While[MemberQ[l, k], k++ ]; c--; ]; Append[l, k]]; Nest[f, {1}, 75] (* Ray Chandler, Nov 23 2006 *)
Fold[Append[#1, Complement[Range[Log2[#2] + Max[#1]], #1][[Max[FactorInteger[#2][[All, 2]]]]]] &, {1}, Range[2, 72]] (* Ivan Neretin, Aug 29 2017 *)

Crossrefs

Sequence in context: A279338 A279348 A274500 * A344682 A344962 A154444

Adjacent sequences: A123914 A123915 A123916 * A123918 A123919 A123920

Keyword

nonn

Author

Leroy Quet, Nov 19 2006

Extensions

Extended by Ray Chandler, Nov 23 2006

Status

approved