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 1-2 of 2 results.

A121409 Prime numbers p such that p and prime(p) have no common decimal digit and prime(p) and prime(prime(p)) have no common decimal digit.

Original entry on oeis.org

2, 3, 17, 19, 89, 317, 563, 1091, 2099, 3181, 5023, 44221, 53899, 410747, 410801, 448373, 451181, 481133, 519151, 617657, 738523, 882979, 992087, 1611433, 2167421, 2688299, 2723627, 2811089, 3331033, 3411043, 3499411, 3983911, 3988889, 6233933
Offset: 1

Views

Author

Zak Seidov, Jul 28 2006

Keywords

Comments

Subsequence of A119405. Positions of a(n) in A119405: A121410.

Examples

			992087 is a term because p(992087)=15353531, p(15353531)=282479297, and 992087 and 15353531 have no common decimal digit, nor do 15353531 and 282479297.

Crossrefs

Cf. A119405, A121410.

Programs

  • Mathematica
    Select[Prime[Range[10^6]],ContainsNone[IntegerDigits[#],IntegerDigits[Prime[#]]]&&ContainsNone[IntegerDigits[Prime[#]],IntegerDigits[Prime[Prime[#]]]]&] (* James C. McMahon, Oct 18 2024 *)

A121470 Expansion of x*(1+5*x+2*x^2+x^3)/((1+x)*(1-x)^3).

Original entry on oeis.org

1, 7, 16, 31, 49, 73, 100, 133, 169, 211, 256, 307, 361, 421, 484, 553, 625, 703, 784, 871, 961, 1057, 1156, 1261, 1369, 1483, 1600, 1723, 1849, 1981, 2116, 2257, 2401, 2551, 2704, 2863, 3025, 3193, 3364, 3541, 3721, 3907, 4096, 4291, 4489, 4693, 4900
Offset: 1

Views

Author

Roger L. Bagula, Sep 07 2006

Keywords

Links

Crossrefs

Cf. A003215, A005448.

Programs

  • Maple
    A121410 := proc(nmin) local M,a,v, wev,wod,n ; a := [] ; M := linalg[matrix](2,2,[0,1,-1,2]) ; v := linalg[vector](2,[1,7]) ; wev := linalg[vector](2,[0,3]) ; wod := linalg[vector](2,[0,6]) ; while nops(a) < nmin do a := [op(a),v[1]] ; n := nops(a)+1 ; v := evalm(M &* v) ; if n mod 2 = 0 then v := evalm(v+wev) ; else v := evalm(v+wod) ; fi ; od: RETURN(a) ; end: A121410(80) ; # R. J. Mathar, Sep 18 2007
  • Mathematica
    M := {{0, 1}, {-1, 2} } v[1] = {1, 7} w[n_] = If[Mod[n, 2] == 0, {0, 3}, {0, 6}] v[n_] := v[n] = M.v[n - 1] + w[n] a = Table[v[n][[1]], {n, 1, 30}]
CoefficientList[Series[x (1+5x+2x^2+x^3)/((1+x)(1-x)^3),{x,0,50}],x] (* or *) LinearRecurrence[{2,0,-2,1},{1,7,16,31},50] (* Harvey P. Dale, Mar 10 2017 *)

Formula

From R. J. Mathar, Jul 10 2009: (Start)
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) = 5/8 - 3n/2 + 9n^2/4 + 3*(-1)^n/8.
G.f.: x*(1+5*x+2*x^2+x^3)/((1+x)*(1-x)^3). (End)

Extensions

Edited by N. J. A. Sloane, Sep 16 2006
More terms from R. J. Mathar, Sep 18 2007
New name from Joerg Arndt, Jun 28 2013
Showing 1-2 of 2 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.