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A160717
Cyclops triangular numbers.
9
0, 105, 406, 703, 903, 11026, 13041, 14028, 15051, 27028, 36046, 41041, 43071, 46056, 61075, 66066, 75078, 77028, 83028, 85078, 93096, 1110795, 1130256, 1160526, 1180416, 1250571, 1290421, 1330896, 1350546, 1360425, 1380291
OFFSET
1,2
COMMENTS
Triangular numbers (A000217) that are also cyclops numbers (A134808).
EXAMPLE
105 is in the sequence since it is both a triangular number (105 = 1 + 2 + ... + 14) and a Cyclops number (number of digits is odd, and the only zero is the middle digit). - Michael B. Porter, Jul 08 2016
MAPLE
count:= 1: A[1]:= 0:
for d from 1 to 3 do
for x from 0 to 9^d-1 do
L:= convert(x+9^d, base, 9);
X:= add((L[i]+1)*10^(i-1), i=1..d);
for y from 0 to 9^d-1 do
L:= convert(y+9^d, base, 9);
Y:= add((L[i]+1)*10^(i-1), i=1..d);
Z:= Y + 10^(d+1)*X;
if issqr(1+8*Z) then
count:= count+1;
A[count]:= Z;
fi
od od od:
seq(A[i], i=1..count); # Robert Israel, Jul 08 2016
MATHEMATICA
cyclopsQ[n_] := Block[{id=IntegerDigits@n, lg=Floor[Log[10, n]+1]}, Count[id, 0]==1 && OddQ@lg && id[[(lg+1)/2]]==0]; lst = {0}; Do[t = n (n + 1)/2; If[ cyclopsQ@t, AppendTo[lst, t]], {n, 0, 1670}]; lst (* Robert G. Wilson v, Jun 09 2009 *)
cyclpsQ[n_]:=With[{len=IntegerLength[n]}, OddQ[len]&&DigitCount[n, 10, 0]==1&&IntegerDigits[n][[(len+1)/2]]==0]; Join[{0}, Select[ Accumulate[ Range[2000]], cyclpsQ]] (* Harvey P. Dale, Nov 05 2024 *)
KEYWORD
base,easy,nonn
AUTHOR
Omar E. Pol, Jun 08 2009
EXTENSIONS
More terms from Robert G. Wilson v, Jun 09 2009
Offset and b-file changed by N. J. A. Sloane, Jul 27 2016
STATUS
approved