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

6, 66, 666, 426426, 266262426, 22464262666, 46624464466426, 644644226644644222426, 46424226426466426446424262644446, 626644642222466644646226466422666

Offset: 1

Author

Giovanni Resta, May 10 2006

Keywords

• nonn
• base
• more

Comments

All terms end in 6. - Robert Israel, Feb 05 2016

a(11) > 10^40. - Tyler Busby, Mar 29 2023

Links

• Giovanni Resta, Tridigital Triangular Numbers.

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