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 1-4 of 4 results.

A055498 a(0)=0, a(1)=1, a(n) = smallest prime >= a(n-1) + a(n-2).

Original entry on oeis.org

0, 1, 2, 3, 5, 11, 17, 29, 47, 79, 127, 211, 347, 563, 911, 1481, 2393, 3877, 6271, 10151, 16427, 26591, 43019, 69623, 112643, 182279, 294923, 477209, 772139, 1249361, 2021501, 3270863, 5292367, 8563237, 13855607, 22418849, 36274471, 58693331, 94967809, 153661163
Offset: 0

Views

Author

N. J. A. Sloane, Jul 08 2000

Keywords

Examples

			After 3, 5, the next prime >=8 is 11.

Links

Crossrefs

Cf. A073021, A073022, A055499, A055500, A055501, A055502.
Cf. A007918.

Programs

  • Haskell
    a055498 n = a055498_list !! n
a055498_list = 0 : 1 : map a007918
    (zipWith (+) a055498_list $ tail a055498_list)
-- Reinhard Zumkeller, Nov 13 2014
  • Mathematica
    a[0] = 0; a[1] = 1; a[n_] := a[n] = NextPrime[a[n - 1] + a[n - 2] -1]; Array[a, 37, 0] (* Robert G. Wilson v, Mar 13 2013 *)
RecurrenceTable[{a[0]==0,a[1]==1,a[n]==NextPrime[a[n-1]+a[n-2]-1]},a,{n,50}] (* Harvey P. Dale, May 08 2013 *)
  • PARI
    a(n)=local(v);if(n<2,n>=0,n++;v=vector(n,i,1);for(i=3,n,v[i]=nextprime(v[i-1]+v[i-2]));v[n]) /* Michael Somos, Feb 01 2004 */

Formula

a(n+1) = nextprime(a(n) + a(n-1)) where nextprime(n) is smallest prime >= n.
a(n) is asymptotic to c*phi^n where phi = (1 + sqrt(5))/2 and c = 1.086541275044988562375... - Benoit Cloitre, May 02 2004
a(n) = A055499(n-1) for n>3. - Robert G. Wilson v, Mar 13 2013
a(n) = A007918(a(n-1) + a(n-2)) for n > 1. - Reinhard Zumkeller, Nov 13 2014

A055502 a(0)=0, a(1)=2, a(n) = smallest prime > a(n-1)+a(n-2).

Original entry on oeis.org

0, 2, 3, 7, 11, 19, 31, 53, 89, 149, 239, 389, 631, 1021, 1657, 2683, 4349, 7039, 11393, 18433, 29833, 48271, 78121, 126397, 204521, 330943, 535481, 866431, 1401937, 2268377, 3670319, 5938711, 9609031, 15547769, 25156811, 40704589, 65861461, 106566059, 172427531
Offset: 0

Views

Author

N. J. A. Sloane, Jul 09 2000

Keywords

Links

Crossrefs

Cf. A055498, A055499, A055500, A055501.

Programs

  • Maple
    A055502 := proc(n) option remember; if n<=0 then n else nextprime(A055502(n-1)+A055502(n-2)); fi; end;
  • Mathematica
    a[0] = 0; a[1] = 2; a[n_] := a[n] = NextPrime[a[n-1] + a[n-2]]; Array[a, 40, 0] (* Amiram Eldar, Sep 24 2023 *)

Extensions

More terms from Amiram Eldar, Sep 24 2023

A055499 a(0)=0, a(1)=1, a(n) = smallest prime > a(n-1)+a(n-2).

Original entry on oeis.org

0, 1, 2, 5, 11, 17, 29, 47, 79, 127, 211, 347, 563, 911, 1481, 2393, 3877, 6271, 10151, 16427, 26591, 43019, 69623, 112643, 182279, 294923, 477209, 772139, 1249361, 2021501, 3270863, 5292367, 8563237, 13855607, 22418849, 36274471, 58693331, 94967809, 153661163
Offset: 0

Views

Author

N. J. A. Sloane, Jul 08 2000

Keywords

Links

Crossrefs

Cf. A055498, A055500, A055501, A055502.

Programs

  • Mathematica
    a[0] = 0; a[1] = 1; a[n_] := a[n] = NextPrime[a[n - 1] + a[n - 2]]; Array[a, 36, 0] (* Robert G. Wilson v, Mar 13 2013 *)

A126092 a(1)=2, a(2)=3, a(3)=5; a(n) = largest prime < a(n-1)+a(n-2)+a(n-3).

Original entry on oeis.org

2, 3, 5, 7, 13, 23, 41, 73, 131, 241, 443, 811, 1493, 2741, 5039, 9257, 17033, 31327, 57601, 105953, 194869, 358417, 659237, 1212521, 2230159, 4101907, 7544573, 13876601, 25523011, 46944179, 86343787, 158810947, 292098907, 537253631
Offset: 1

Views

Author

Zak Seidov, Mar 03 2007

Keywords

Links

Crossrefs

Cf. A055501.

Programs

  • Maple
    f:= proc(n) option remember; prevprime(procname(n-1)+procname(n-2)+procname(n-3)) end proc:
f(1):= 2: f(2):= 3: f(3):= 5:
map(f, [$1..100]); # Robert Israel, Mar 12 2018
  • Mathematica
    nxt[{a_,b_,c_}]:={b,c,NextPrime[a+b+c,-1]}; NestList[nxt,{2,3,5},40][[All,1]] (* Harvey P. Dale, Jun 09 2018 *)
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.