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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
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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Nov 19 2006
EXTENSIONS
Extended by Ray Chandler, Nov 23 2006
STATUS
approved