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A119160
Triangular numbers composed of digits {2,4,6}.
2
6, 66, 666, 426426, 266262426, 22464262666, 46624464466426, 644644226644644222426, 46424226426466426446424262644446, 626644642222466644646226466422666
OFFSET
1,1
COMMENTS
All terms end in 6. - Robert Israel, Feb 05 2016
a(11) > 10^40. - Tyler Busby, Mar 29 2023
FORMULA
a(n) = A000217(A119161(n)). - Tyler Busby, Mar 29 2023
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*)
PROG
(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
CROSSREFS
Cf. A000217, A053923, A119161. See A119033 for a table of cross-references.
Sequence in context: A119089 A036523 A112902 * A119210 A227220 A119234
KEYWORD
nonn,base,more
AUTHOR
Giovanni Resta, May 10 2006
EXTENSIONS
a(10) from Max Alekseyev, Jun 16 2011
STATUS
approved