

A125844


a(n) = the smallest positive integer which does not occur earlier in the sequence and which is coprime to the nth composite integer.


0



1, 5, 3, 2, 7, 11, 9, 4, 13, 17, 19, 8, 15, 23, 6, 21, 10, 25, 29, 27, 14, 31, 12, 35, 33, 16, 37, 41, 39, 22, 43, 47, 18, 49, 20, 45, 53, 24, 51, 26, 55, 59, 57, 32, 61, 28, 65, 63, 34, 67, 71, 69, 38, 73, 30, 77, 79, 40, 75, 83, 36, 81, 44, 85, 89, 46, 87, 50, 91, 42, 95, 93
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OFFSET

1,2


COMMENTS

This sequence is a permutation of the positive integers.


LINKS

Table of n, a(n) for n=1..72.


EXAMPLE

The positive integers which do not occur among the first 6 terms of the sequence are 4,6,8,9,10,12,... Of these integers, 9 is the smallest that is coprime to 14, the 7th composite. So a(7) = 9.


MATHEMATICA

f[l_List] := Block[{n = Length[l] + 1, c = 1, k = n}, While[k > 0, c++; While[PrimeQ[c], c++ ]; k; ]; k = 1; While[MemberQ[l, k]  GCD[k, c] > 1, k++ ]; Append[l, k]]; Nest[f, {}, 75] (*Chandler*)


CROSSREFS

Cf. A002808.
Sequence in context: A009661 A023576 A271523 * A171025 A222362 A176524
Adjacent sequences: A125841 A125842 A125843 * A125845 A125846 A125847


KEYWORD

nonn


AUTHOR

Leroy Quet, Feb 03 2007


EXTENSIONS

Extended by Ray Chandler, Feb 07 2007


STATUS

approved



