cp's OEIS Frontend

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

%I A119160 #27 Apr 06 2023 20:07:56
%S A119160 6,66,666,426426,266262426,22464262666,46624464466426,
%T A119160 644644226644644222426,46424226426466426446424262644446,
%U A119160 626644642222466644646226466422666
%N A119160 Triangular numbers composed of digits {2,4,6}.
%C A119160 All terms end in 6. - _Robert Israel_, Feb 05 2016
%C A119160 a(11) > 10^40. - _Tyler Busby_, Mar 29 2023
%H A119160 Giovanni Resta, <a href="http://www.numbersaplenty.com/tr/tr246.html">Tridigital Triangular Numbers</a>.
%F A119160 a(n) = A000217(A119161(n)). - _Tyler Busby_, Mar 29 2023
%p A119160 F:= proc(d) # get all terms with d digits
%p A119160 local res, m, prefs,i,t,qmax,qmin,smax,smin,cand,s;
%p A119160   res:= NULL;
%p A119160   m:= max(1,floor(d/2-1));
%p A119160   prefs:= [2,4,6]*10^(d-1);
%p A119160   for i from 1 to m-1 do
%p A119160     prefs:= map(t -> (t + 2*10^(d-1-i),t+4*10^(d-1-i),t+6*10^(d-1-i)), prefs)
%p A119160   od;
%p A119160   for t in prefs do
%p A119160        qmax:= t + 6*(10^(d-m)-1)/9; smax:= floor(sqrt(8*qmax+1));
%p A119160        qmin:= t + 2*(10^(d-m)-1)/9; smin:= ceil(sqrt(8*qmin+1));
%p A119160        smin:= smin + 1 - (smin mod 2);
%p A119160        for s from smin to smax by 2 do
%p A119160            cand:= (s^2 -1)/8;
%p A119160            if cand mod 10 = 6 and convert(convert(cand,base,10),set) subset {2,4,6} then
%p A119160               res:= res, cand;
%p A119160            fi
%p A119160        od
%p A119160   od;
%p A119160 res;
%p A119160 end proc:
%p A119160 seq(F(d),d=1..21);  # _Robert Israel_, Feb 05 2016
%t A119160 Select[#*(# + 1)/2 & /@
%t A119160   Range[1000000], !
%t A119160 MemberQ[IntegerDigits[#], 0 | 1 | 3 | 5 | 7 | 8 | 9] &] (*_Julien Kluge_, Feb 01 2016*)
%o A119160 (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
%Y A119160 Cf. A000217, A053923, A119161. See A119033 for a table of cross-references.
%K A119160 nonn,base,more
%O A119160 1,1
%A A119160 _Giovanni Resta_, May 10 2006
%E A119160 a(10) from _Max Alekseyev_, Jun 16 2011