A125844 a(n) = the smallest positive integer which does not occur earlier in the sequence and which is coprime to the n-th composite integer.

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

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] (* Ray Chandler, Feb 07 2007 *)

Crossrefs

Cf. A002808.

Sequence in context: A023576 A271523 A352903 * A171025 A222362 A352024

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