A094339 Beginning with 2, least number not occurring earlier that divides the sum of all previous terms.

2, 1, 3, 6, 4, 8, 12, 9, 5, 10, 15, 25, 20, 24, 16, 32, 48, 30, 18, 36, 27, 13, 7, 53, 106, 265, 159, 318, 212, 14, 107, 321, 214, 428, 642, 535, 35, 21, 181, 11, 33, 22, 23, 59, 70, 28, 151, 29, 19, 233, 466, 2563, 699, 932, 40, 26, 38, 31, 61, 39, 49, 98, 42, 56, 50, 197, 17

Offset

1,1

Comments

Conjecture: this is a rearrangement of natural numbers.

Comments from Zak Seidov, Feb 19 2005:

"Changing the seed produces different sequences, some of which merge into each other:

s2=2,1,3,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53

s3=3,1,2,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53

s4=4,1,5,2,3,15,6,9,45,10,20,8,16,12,13,169,26,7,53,106,265,159,18

s5=5,1,2,4,3,15,6,9,45,10,20,8,16,12,13,169,26,7,53,106,265,159,18

s6=6,1,7,2,4,5,25,10,3,9,8,16,12,18,14,20,32,24,27,81,36,15,75,30,40

s7=7,1,2,5,3,6,4,14,21,9,8,10,15,35,20,16,11,17,12,18,13,19,38,76,95

s8=8,1,3,2,7,21,6,4,13,5,10,16,12,9,39,26,14,28,32,64,20,17,51,24,18

s9=9,1,2,3,5,4,6,10,8,12,15,25,20,24,16,32,48,30,18,36,27,13,7,53,106

s10=10,1,11,2,3,9,4,5,15,6,22,8,12,18,7,19,38,95,57,114,24,16,31,17,32

s11=11,1,2,7,3,4,14,6,8,28,12,16,56,21,9,18,24,5,35,10,29,319,22,15,25,20,30

In every case one may ask if the result is a rearrangement of the natural numbers."

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

The sum of first 7 terms is 36, hence a(8) = 9 is the least divisor of 36 not occurring earlier.

Maple

A094339 := proc(nmax) local a, n, sprev, i; a := [2] ; while nops(a) < nmax do sprev := add(i, i=a) ; n := 1 ; while sprev mod n <> 0 or n in a do n := n+1 ; od ; a := [op(a), n] ; od ; RETURN(a) ; end: A094339(100) ; # R. J. Mathar, Apr 30 2007

Mathematica

a={2}; Do[AppendTo[a, Min[Select[Divisors[Plus@@a], !MemberQ[a, #]&]]], {t, 2, 70}]; a (* Ivan Neretin, Apr 13 2015 *)

Prog

(PARI) v=[2]; n=1; while(#v<100, if(!vecsearch(vecsort(v, , 8), n)&&!(vecsum(v)%n), v=concat(v, n); n=0); n++); v \\ Derek Orr, Apr 13 2015

Crossrefs

Cf. A094340, A094341.

Sequence in context: A340406 A257881 A268182 * A317788 A120576 A063707

Adjacent sequences: A094336 A094337 A094338 * A094340 A094341 A094342

Keyword

nonn

Author

Amarnath Murthy, May 17 2004

Extensions

Corrected and extended by R. J. Mathar, Apr 30 2007

Status

approved