cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Amarnath Murthy, May 17 2004

Keywords

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

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

A094340 a(n) = n-th partial sum of A094339 divided by A094339(n+1).

Original entry on oeis.org

2, 1, 1, 3, 2, 2, 4, 9, 5, 4, 3, 5, 5, 9, 5, 4, 8, 15, 8, 12, 27, 52, 7, 4, 2, 5, 3, 6, 106, 14, 5, 9, 5, 4, 6, 107, 180, 21, 362, 121, 183, 176, 69, 59, 150, 28, 151, 232, 19, 10, 2, 11, 9, 233, 360, 247, 304, 155, 244, 195, 98, 231, 174, 196, 50, 591, 296, 198, 51, 199, 160, 115
Offset: 1

Views

Author

Amarnath Murthy, May 17 2004

Keywords

Comments

Conjecture: Every natural number occurs in this sequence.

Crossrefs

Cf. A094339, 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: A094340 := proc(a094339,n) add( op(i,a094339),i=1..n)/op(n+1,a094339) ; end: a094339 := A094339(100) ; for n from 1 to nops(a094339)-1 do printf("%d, ", A094340(a094339,n)) ; od ; # R. J. Mathar, Apr 30 2007

Extensions

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

A109736 Where n appears in A109890.

Original entry on oeis.org

1, 2, 3, 5, 9, 4, 23, 6, 8, 10, 40, 7, 22, 30, 11, 15, 67, 19, 49, 13, 38, 42, 43, 14, 12, 56, 21, 46, 48, 18, 58, 16, 41, 68, 37, 20, 89, 57, 60, 55, 76, 63, 151, 78, 107, 96, 98, 17, 61, 65, 69, 71, 24, 103, 87, 64, 80, 74, 44, 83, 59, 92, 101, 94, 72, 91, 185, 142, 104, 45
Offset: 1

Views

Author

N. J. A. Sloane and Nadia Heninger, Aug 11 2005

Keywords

Comments

a(10^n): 1, 10, 128, 1430, ... - Robert G. Wilson v, Aug 12 2005
a(n) = A094341(n) for 3 <= n <= 70. - Georg Fischer, Nov 02 2018
According to the remarks in A109890, A094339 and A109890 are essentially the same, just swapping the first 2 terms, so this here is a(n)=A094341(n) for n>=3. - R. J. Mathar, Jul 02 2025

Links

Crossrefs

Cf. A094341, A095259, A109890.

Programs

  • Haskell
    import Data.List (elemIndex); import Data.Maybe (fromJust)
a109736 = (+ 1) . fromJust . (`elemIndex` a109890_list)
-- Reinhard Zumkeller, Jan 01 2015
  • Mathematica
    a[1] = 1; a[2] = 2; a[n_] := a[n] = Block[{t = Table[a[i], {i, n - 1}]}, s = Plus @@ t; d = Divisors[s]; l = Complement[d, t]; If[l != {}, k = First[l], k = s; While[Position[t, k] == {}, k += s]; k]]; t = Table[a[n], {n, 250}]; Table[k = 1; While[ t[[k]] != n, k++ ]; k, {n, 70}] (* Robert G. Wilson v, Aug 12 2005 *)

Extensions

More terms from Robert G. Wilson v, Aug 12 2005
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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