A073929 a(1) = 1, a(n) = smallest number not included earlier such that the n-th partial sum (n>1) is divisible by n+1.

1, 2, 5, 7, 3, 10, 4, 13, 15, 6, 18, 20, 8, 23, 9, 26, 28, 11, 31, 12, 34, 36, 14, 39, 41, 16, 44, 17, 47, 49, 19, 52, 54, 21, 57, 22, 60, 62, 24, 65, 25, 68, 70, 27, 73, 75, 29, 78, 30, 81, 83, 32, 86, 33, 89, 91, 35, 94, 96, 37, 99, 38, 102, 104, 40, 107, 109, 42, 112, 43

Offset

1,2

Comments

a(n) = A002251(n) for 2 < n < 10000. - Georg Fischer, Oct 19 2018

Links

R. J. Cano, Table of n, a(n) for n = 1..10000

Example

4 divides 1+2+5, but does not divide 1+2+3 or 1+2+4, so a(3)=5.

Maple

s := {1}:summe := 1:a[1] := 1:for j from 2 to 1000 do b := (j+1)-(summe mod (j+1)); i := 0:while(true) do if nops(s union {b+i*(j+1)})-nops(s)=1 then break; fi; i := i+1; od:a[j] := b+i*(j+1):s := s union {b+i*(j+1)}:summe := summe+a[j]:od:c := seq(a[k], k=1..1000);

Mathematica

Nest[Append[#, Block[{k = 2}, While[Nand[FreeQ[#, k], Mod[Total@ # + k, Length@ # + 2] == 0], k++]; k]] &, {1}, 69] (* Michael De Vlieger, May 10 2018 *)

Prog

(PARI) vecA073929(n)={my(w=1, s=List(vector(100*n, u, u)), t); for(m=2, n, for(i=m, #s, if(!((w+s[i])%(m+1)), t=s[i]; w+=t; listpop(s, i); listinsert(s, t, m); break))); Vec(s)[1..n]} \\ R. J. Cano, May 07 2018

Crossrefs

A002251

Sequence in context: A024710 A140264 A140263 * A361329 A076555 A095928

Adjacent sequences: A073926 A073927 A073928 * A073930 A073931 A073932

Keyword

nonn

Author

Amarnath Murthy, Aug 19 2002

Extensions

Corrected and edited by John W. Layman and Sascha Kurz, Aug 21 2002

Offset corrected by R. J. Cano, May 07 2018

Status

approved