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 1-3 of 3 results.

A000336 a(n) = a(n-1)*a(n-2)*a(n-3)*a(n-4); for n < 5, a(n) = n.

Original entry on oeis.org

1, 2, 3, 4, 24, 576, 165888, 9172942848, 21035720123168587776, 18437563379178327736384102280592359424, 590180110002114158896983994712576414865667267958188575935810179040280576
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

The next term has 139 digits. - Harvey P. Dale, Jan 21 2019

Links

Crossrefs

Cf. A000301, A000308, A001631, A003586, A251656.

Programs

  • Maple
    A000336 := proc(n) option remember; if n <=4 then n else A000336(n-1)*A000336(n-2)*A000336(n-3)*A000336(n-4); fi; end;
  • Mathematica
    t = {1, 2, 3, 4}; Do[AppendTo[t, t[[-1]]*t[[-2]]*t[[-3]]*t[[-4]]], {n, 5, 15}] (* T. D. Noe, Jun 19 2012 *)
nxt[{a_,b_,c_,d_}]:={b,c,d,a b c d}; NestList[nxt,{1,2,3,4},10][[All,1]] (* Harvey P. Dale, Jan 21 2019 *)
  • PARI
    a(n,a=[24,1,2,3,4])={for(n=6,n,a[n%5+1]=a[(n-1)%5+1]^2\a[n%5+1]);a[n%5+1]} \\ M. F. Hasler, Apr 22 2018
  • PARI
    first(n) = n = max(n, 5); my(res = vector(n)); for(i=1, 4, res[i] = i); res[5]=24; for(i = 6, n, res[i] = res[i-1]^2 / res[i - 5]); res \\ David A. Corneth, Apr 22 2018

Formula

a(n) = 2^A251656(n) * 3^A001631(n-1). - Vaclav Kotesovec, Feb 02 2016
a(n) = a(n-1)^2 / a(n-5), for n > 5. - M. F. Hasler, Apr 22 2018

A063401 a(n) = a(n-1)*a(n-2)*a(n-3) with a(0)=1, a(1)=2, a(2)=2.

Original entry on oeis.org

1, 2, 2, 4, 16, 128, 8192, 16777216, 17592186044416, 2417851639229258349412352, 713623846352979940529142984724747568191373312, 30354201441027016733116592294117482916287606860189680019559568902170379456331382784
Offset: 0

Views

Author

Henry Bottomley, Jul 16 2001

Keywords

Examples

			a(6) = 128*16*4 = 8192.

Links

Crossrefs

Cf. A000301, A000308.

Programs

  • Mathematica
    a0=1;a1=1;a2=2;lst={a0,a1,a2};Do[AppendTo[lst,a=a0*a1*a2]; a0=a1;a1=a2;a2=a, {n,12}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 18 2009 *)
RecurrenceTable[{a[0]==1,a[1]==a[2]==2,a[n]==a[n-1]a[n-2]a[n-3]},a,{n,12}] (* Harvey P. Dale, Sep 05 2021 *)
  • PARI
    { for (n = 0, 15, if (n>2, a=a1*a2*a3; a3=a2; a2=a1; a1=a, if (n==0, a=a3=1; a1=a2=2, a=2)); write("b063401.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 20 2009

Formula

a(n) = 2^A000073(n+1).

Extensions

Definition corrected to a(1)=2 by Harry J. Smith, Aug 20 2009

A299399 a(n) = a(n-1)*a(n-2)*a(n-3)*a(n-4); a(0..3) = (1, 1, 2, 3).

Original entry on oeis.org

1, 1, 2, 3, 6, 36, 1296, 839808, 235092492288, 9211413321697223245824, 2356948205087252000835395074931259831484416, 4286423488783965214900384842824017360544199884413056912194095171350270745233063936
Offset: 0

Views

Author

M. F. Hasler, Apr 22 2018

Keywords

Comments

A variant of A000336 which uses initial values (1,2,3,4).
A multiplicative variant of the tetranacci sequences A000078, A001631 and other variants.

Links

Crossrefs

Cf. A000336 (variant starting 1,2,3,4).
Cf. A000301 (order 2 variant), A000308 (order 3 variant).
Subsequence of A003586 (3-smooth numbers).
Cf. A000078, A001631 (additive variants).

Programs

  • Mathematica
    nxt[{a_,b_,c_,d_}]:={b,c,d,a b c d}; NestList[nxt,{1,1,2,3},13][[All,1]] (* Harvey P. Dale, Jun 09 2022 *)
  • PARI
    A299399(n,a=[1,1,2,3,6])={for(n=5,n,a[n%#a+1]=a[(n-1)%#a+1]^2\a[n%#a+1]);a[n%#a+1]}

Formula

a(n) = a(n-1)^2 / a(n-5) for n > 4.
a(n) = 2^A001631(n)*3^A000078(n).
Showing 1-3 of 3 results.

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

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