A075085 a(n) is the smallest number not already in the sequence such that Sum_{k=1..n} a(k) is divisible by prime(n).

2, 1, 7, 4, 8, 17, 12, 6, 35, 24, 39, 30, 20, 10, 67, 36, 95, 14, 42, 28, 87, 48, 32, 137, 72, 238, 22, 44, 131, 161, 55, 179, 78, 26, 130, 177, 84, 247, 60, 90, 269, 213, 170, 34, 68, 233, 5, 204, 295, 265, 76, 114, 38, 190, 371, 120, 389, 313, 132, 88, 327, 230, 15, 399

Offset

1,1

Comments

Original title: Rearrangement of natural numbers such that the n-th partial sum is divisible by the n-th prime.

The numbers 3, 9, 13, ... do not appear in the first 1655 terms of this sequence. Is this truly a permutation of the natural numbers? - Derek Orr, Jun 16 2015

a(100959)=13. - Alois P. Heinz, Jun 17 2015

The numbers 3, 9, 16, 18, 19, ... do not appear in the first 80 million terms of this sequence - Carl R. White, Mar 07 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Carl R. White, C source to generate 80 million terms

Maple

b:= proc() false end:
s:= proc(n) option remember; a(n)+s(n-1) end: s(0):=0:
a:= proc(n) option remember; local k, p; p:= ithprime(n);
      for k from p*(iquo(s(n-1), p)+1)-s(n-1)
        while b(k) by p do od; b(k):= true; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 17 2015

Mathematica

f[lst_] := Block[{k = 1, p = Prime[1 + Length@ lst], s = Total@ lst}, While[Mod[s + k, p] != 0 || MemberQ[lst, k], k++]; Append[lst, k]]; Nest[f, {}, 64] (* Robert G. Wilson v, Jun 17 2015 *)

Prog

(PARI) v=[2]; n=1; while(n<10^3, s=(n+vecsum(v))%prime(#v+1); if(!(s||vecsearch(vecsort(v), n)), v=concat(v, n); n=0); n++); v \\ Derek Orr, Jun 16 2015

Crossrefs

Sequence in context: A089225 A185110 A343202 * A217458 A124048 A087059

Adjacent sequences: A075082 A075083 A075084 * A075086 A075087 A075088

Keyword

nonn,look

Author

Amarnath Murthy, Sep 13 2002

Extensions

More terms from David Wasserman, Jan 16 2005

Status

approved