A119142
Triangular numbers composed of digits {1,6,8}.
Original entry on oeis.org
1, 6, 66, 666, 861, 116886, 1188111, 8166861, 681118686, 8186688861, 181886818816, 616886668881, 1611611188111, 6188181818668868161, 8188686181116816661, 61116116118118668181, 686168618118116111616, 1118166618111681811816, 66861818861688166881668181
Offset: 1
A119144
Triangular numbers composed of digits {1,6,9}.
Original entry on oeis.org
1, 6, 66, 91, 666, 961191, 996166, 1191196, 96111966961, 99119996661, 16161696119661, 196999111911966, 661969169911666, 11961669169169616, 19961691661699161, 991961666199161911, 6116119911196616916, 16961161696691611916961, 911666691991111199916696
Offset: 1
A119146
Triangular numbers composed of digits {1,7,8}.
Original entry on oeis.org
1, 78, 171, 1711, 8778, 11781, 887778, 1188111, 18111171, 71778171, 88877778, 811178781, 7781717881, 8888777778, 181877771881, 887788118778, 888887777778, 88877878118778, 88888877777778, 181887881178871, 8888778778118778, 8888888777777778, 117888788817817111
Offset: 1
A119148
Triangular numbers composed of digits {1,7,9}.
Original entry on oeis.org
1, 91, 171, 1711, 171991, 791911, 1717771191, 911977119991, 999999911791, 1771177919779971, 977779999771199191, 17979999719799917971, 7197199171171779119991779991
Offset: 1
A119150
Triangular numbers composed of digits {1,8,9}.
Original entry on oeis.org
1, 91, 1891, 8911, 188191, 889111, 899811, 998991, 1188111, 11899881, 88891111, 1918188891, 8888911111, 9998888991, 189889118191, 191819818191, 199198198891, 888889111111, 88888891111111, 8888888911111111, 888888889111111111, 88888888891111111111
Offset: 1
A119152
Triangular numbers composed of digits {2,3,5}.
Original entry on oeis.org
3, 55, 253, 325, 5253, 255255, 2235555, 2355535, 3252525, 222552253, 225323523253, 33533553332223253, 523355323323222253, 252235353552533225335, 22323332525535322225335, 223533355523232355353232325353525335
Offset: 1
A119154
Triangular numbers composed of digits {2,3,6}.
Original entry on oeis.org
3, 6, 36, 66, 666, 22366, 333336, 23232336, 336662326, 2232222336, 3263633236, 6266233326, 262322266326, 266633626626, 2263263223266, 36226633633326, 66333362366236266, 3236622262232626626666, 3322222636222323322336, 2332636666226262326336266
Offset: 1
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Select[Flatten[Table[FromDigits/@Tuples[{2,3,6},n],{n,10}]],OddQ[Sqrt[8#+1]]&] (* The program generates the first 12 terms of the sequence. To generate more, increase the constant after "n," but the program will take longer to run. *) (* Harvey P. Dale, Apr 18 2020 *)
A119156
Triangular numbers composed of digits {2,3,8}.
Original entry on oeis.org
3, 28, 3828, 828828, 388333828828, 223832333328828, 332828222833288828828, 28388332838238232223328828
Offset: 1
A119158
Triangular numbers composed of digits {2,4,5}.
Original entry on oeis.org
45, 55, 25425, 255255, 22542255, 244525555, 2245524452445, 2445254445525, 5255545252454245, 444222245455224445, 4544525455555255444225, 5554545454254522254255544522452525245
Offset: 1
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
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[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
-
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
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Select[#*(# + 1)/2 & /@
Range[1000000], !
MemberQ[IntegerDigits[#], 0 | 1 | 3 | 5 | 7 | 8 | 9] &] (*Julien Kluge, Feb 01 2016*)
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