A117532 a(n) = smallest positive integer not occurring earlier in the sequence such that Sum_{k=1..n} a(k) is coprime to n.

1, 2, 4, 6, 3, 7, 8, 10, 5, 11, 12, 14, 9, 15, 17, 13, 18, 20, 16, 22, 19, 23, 24, 26, 21, 27, 29, 25, 30, 32, 28, 34, 31, 35, 36, 38, 33, 39, 41, 37, 42, 44, 40, 46, 43, 47, 48, 50, 45, 51, 53, 49, 54, 56, 52, 58, 55, 59, 60, 64, 57, 61, 62, 66, 63, 67, 68, 70, 65, 71, 72, 74

Offset

1,2

Comments

Sequence is likely to be a permutation of the positive integers, but I am uncertain. A117533(n) = Sum_{k=1..n} a(k). Sequence A117534 is the inverse permutation if this sequence is a permutation of the positive integers.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3000

Example

a(4) = 6 because 6 is the smallest positive integer m not among the first 3 terms of the sequence such that 1+2+4+m is coprime to 4. 1+2+4+3 = 10 and gcd(4,10)=2; 1+2+4+5 = 12 and gcd(4,12)=4; but 1+2+4+6 = 13 and gcd(4,13)=1.

Maple

A117532 := proc(nmax) local a, n, nxt, asu ; a := [1] ; asu := 1 ; while nops(a) < nmax do n := nops(a)+1 ; nxt := 1 ; while nxt in a or gcd(n, asu+nxt) <> 1 do nxt := nxt+1 ; od ; a := [op(a), nxt] ; asu := asu+nxt ; od ; a ; end: A117532(80) ; # R. J. Mathar, May 10 2007

Mathematica

Fold[Append[#1, Block[{k = 2}, While[Nand[FreeQ[#1, k], CoprimeQ[Total@ #1 + k, #2]], k++]; k]] &, {1}, Range[2, 72]] (* Michael De Vlieger, Sep 30 2017 *)

Crossrefs

Cf. A117534, A117533.

Sequence in context: A349543 A140645 A327724 * A287662 A278376 A358209

Adjacent sequences: A117529 A117530 A117531 * A117533 A117534 A117535

Keyword

nonn

Author

Leroy Quet, Mar 26 2006

Extensions

More terms from R. J. Mathar, May 10 2007

Status

approved