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.

A053922 Numbers k such that k^2 contains only digits {2,4,6}.

Original entry on oeis.org

2, 8, 68, 162, 668, 5162, 6668, 25738, 66668, 79162, 163238, 666668, 6666668, 8041408, 24993332, 66666668, 666666668, 6666666668, 8016649092, 66666666668, 666666666668, 6666666666668, 66666666666668
Offset: 1

Views

Author

Patrick De Geest, Mar 15 2000

Keywords

Comments

Conjecture: every number composed of the numeral six repeated n times and ending in the numeral 8 is a term of this sequence. - Harvey P. Dale, Jun 16 2022
From Zhao Hui Du, Mar 11 2024: (Start)
Six repeated n times and ending with 8 can be written as (6/9)*(10^n-1)+2. The square of it can be written as (4/9)*(10^(2*n)-1)+(16/9)*(10^n-1)+4. Or
444444...44444...444
+ 1777...776
+ 4
----------------------
444444...46222...224. (End)

Crossrefs

Cf. A053923.

Programs

  • Mathematica
    Select[Range[700000],SubsetQ[{2,4,6},IntegerDigits[#^2]]&] (* The program generates the first 12 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Jun 16 2022 *)

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 04 2005
Two more terms from Jon E. Schoenfield, Sep 04 2006

A119160 Triangular numbers composed of digits {2,4,6}.

Original entry on oeis.org

6, 66, 666, 426426, 266262426, 22464262666, 46624464466426, 644644226644644222426, 46424226426466426446424262644446, 626644642222466644646226466422666
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Comments

All terms end in 6. - Robert Israel, Feb 05 2016
a(11) > 10^40. - Tyler Busby, Mar 29 2023

Crossrefs

Cf. A000217, A053923, A119161. See A119033 for a table of cross-references.

Programs

  • Magma
    [t: n in [1..2*10^7] | Set(Intseq(t)) subset {2, 4, 6} where t is n*(n+1) div 2]; // Vincenzo Librandi, Feb 04 2016
  • Maple
    F:= proc(d) # get all terms with d digits
    local res, m, prefs,i,t,qmax,qmin,smax,smin,cand,s;
      res:= NULL;
      m:= max(1,floor(d/2-1));
      prefs:= [2,4,6]*10^(d-1);
      for i from 1 to m-1 do
        prefs:= map(t -> (t + 2*10^(d-1-i),t+4*10^(d-1-i),t+6*10^(d-1-i)), prefs)
      od;
      for t in prefs do
           qmax:= t + 6*(10^(d-m)-1)/9; smax:= floor(sqrt(8*qmax+1));
           qmin:= t + 2*(10^(d-m)-1)/9; smin:= ceil(sqrt(8*qmin+1));
           smin:= smin + 1 - (smin mod 2);
           for s from smin to smax by 2 do
               cand:= (s^2 -1)/8;
               if cand mod 10 = 6 and convert(convert(cand,base,10),set) subset {2,4,6} then
                  res:= res, cand;
               fi
           od
      od;
    res;
    end proc:
    seq(F(d),d=1..21);  # Robert Israel, Feb 05 2016
  • Mathematica
    Select[#*(# + 1)/2 & /@
      Range[1000000], !
    MemberQ[IntegerDigits[#], 0 | 1 | 3 | 5 | 7 | 8 | 9] &] (*Julien Kluge, Feb 01 2016*)

Formula

a(n) = A000217(A119161(n)). - Tyler Busby, Mar 29 2023

Extensions

a(10) from Max Alekseyev, Jun 16 2011
Showing 1-2 of 2 results.