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
Examples
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
Links
- Kenny Lau, Table of n, a(n) for n = 1..20001
Programs
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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 *)
Extensions
More terms from Robert G. Wilson v, Jun 09 2009
Offset and b-file changed by N. J. A. Sloane, Jul 27 2016
Comments