A160717 Cyclops triangular numbers.

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).

Links

Kenny Lau, Table of n, a(n) for n = 1..20001

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 *)

Crossrefs

Cf. A000217, A134808, A134809, A138131, A138148, A153806, A160711, A160712.

Sequence in context: A160340 A136418 A134518 * A165056 A165060 A165069

Adjacent sequences: A160714 A160715 A160716 * A160718 A160719 A160720

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