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

Author

Amarnath Murthy, May 17 2004

Keywords

• nonn

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."

Examples

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

Links

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

Crossrefs

Cf. A094340, A094341.

Programs

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 *)

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

Extensions

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