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.

Showing 1-5 of 5 results.

A127646 a(n) is the product of first n terms of sequence A127644.

Original entry on oeis.org

3, 18, 162, 2916, 34992, 559872, 4478976, 107495424, 3439853568, 116955021312, 3508650639360, 168415230689280, 2526228460339200, 2526228460339200, 35367198444748800, 70734396889497600, 1202484747121459200
Offset: 1

Views

Author

Leroy Quet, Jan 22 2007

Keywords

Comments

a(n) is divisible by A127645(n).

Links

Crossrefs

Cf. A127644, A127645.

Programs

  • Mathematica
    f[l_List] := Block[{k = 1, s = Plus @@ l, p = Times @@ l}, While[Or[MemberQ[l, k], Mod[k p, k + s] > 0], k++]; Append[l, k]]; FoldList[Times, Nest[f, {3}, 17]] (* Michael De Vlieger, Sep 20 2017, after Ray Chandler at A127644 *)

Extensions

Extended by Ray Chandler, Jan 22 2007

A127645 a(n) = sum of first n terms of sequence A127644.

Original entry on oeis.org

3, 9, 18, 36, 48, 64, 72, 96, 128, 162, 192, 240, 255, 256, 270, 272, 289, 300, 320, 324, 350, 357, 378, 400, 405, 432, 442, 455, 480, 520, 539, 567, 600, 637, 660, 702, 740, 784, 819, 850, 891, 920, 966, 1015, 1054, 1104, 1140, 1183, 1230, 1275, 1326, 1380
Offset: 1

Views

Author

Leroy Quet, Jan 22 2007

Keywords

Comments

a(n) divides A127646(n).

Crossrefs

Cf. A127644, A127646.

Extensions

Extended by Ray Chandler, Jan 22 2007

A253897 Numbers n such that the sequence A127644 with a(1) = n is conjectured to give a permutation of the natural numbers.

Original entry on oeis.org

3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 36, 39, 40, 44, 45, 48, 50, 55, 56, 60, 63, 66, 70, 72, 75, 77, 78, 80, 84, 88, 90, 91, 99, 102, 104, 105, 108, 112, 117, 120, 126, 130, 132, 135, 140, 144, 150, 154, 160, 165, 168, 176, 180, 182, 195, 198, 208
Offset: 1

Views

Author

Derek Orr, Jan 17 2015

Keywords

Comments

See A127644 for more information.

Examples

			a(1) = 3 because A127644 is conjectured to be a permutation of the natural numbers.

Crossrefs

Cf. A127644, A252984.

Programs

  • PARI
    b(r)=v=[r];n=1;while(n<100,p=prod(i=1,#v,v[i]);if(p*n\(vecsum(v)+n)==p*n/(vecsum(v)+n)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);#v
r=1;while(r<500,if(b(r)>50,print1(r,", "));r++)

A252984 a(0)=4. a(n) is the smallest number not in the sequence such that Sum_{k=1..n} a(k) divides Product_{k=1..n} a(k).

Original entry on oeis.org

4, 12, 8, 24, 6, 10, 16, 20, 25, 3, 7, 5, 22, 13, 1, 19, 14, 11, 27, 9, 17, 2, 29, 15, 21, 23, 28, 34, 30, 31, 18, 35, 33, 26, 32, 37, 36, 38, 39, 45, 42, 43, 40, 49, 41, 48, 46, 44, 47, 50, 51, 54, 55, 53, 52, 56, 57, 62, 61, 60, 64, 68, 67, 58, 63, 70, 69, 71, 65, 77, 66, 72, 74, 73, 59
Offset: 0

Views

Author

Derek Orr, Jan 17 2015

Keywords

Comments

Conjectured to be a permutation of the natural numbers.

Crossrefs

Cf. A127644.

Programs

  • Mathematica
    f[lst_List] := Block[{k = 1, s = Plus @@ lst, p = Times @@ lst}, While[ MemberQ[lst, k] || Mod[p*k, s + k] > 0, k++]; Append[ lst, k]]; Nest[f, {3}, 75] (* Robert G. Wilson v, Jan 19 2015 *)
  • PARI
    v=[4]; print1(4,", ");n=1; while(n<100, p=prod(i=1, #v, v[i]); if(p*n\(vecsum(v)+n)==p*n/(vecsum(v)+n)&&!vecsearch(vecsort(v), n), v=concat(v, n); print1(n, ", "); n=0); n++)

Extensions

Offset corrected by N. J. A. Sloane, Jun 16 2021

A253898 Complement of A253897.

Original entry on oeis.org

1, 2, 7, 11, 13, 17, 19, 23, 25, 26, 27, 29, 31, 32, 34, 37, 38, 41, 42, 43, 46, 47, 49, 51, 52, 53, 54, 57, 58, 59, 61, 62, 64, 65, 67, 68, 69, 71, 73, 74, 76, 79, 81, 82, 83, 85, 86, 87, 89, 92, 93, 94, 95, 96, 97, 98, 100, 101, 103, 106, 107, 109, 110, 111, 113, 114, 115, 116, 118, 119
Offset: 1

Views

Author

Derek Orr, Jan 17 2015

Keywords

Comments

Numbers n such that the sequence A127644 with a(1) = n does not give a permutation of the natural numbers. See A127644 for more information.

Crossrefs

Cf. A127644, A253897.

Programs

  • PARI
    b(r)=v=[r];n=1;while(n<100,p=prod(i=1,#v,v[i]);if(p*n\(vecsum(v)+n)==p*n/(vecsum(v)+n)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);#v
r=1;while(r<100,if(b(r)<50,print1(r,", "));r++)
Showing 1-5 of 5 results.

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

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