A239828 -id:A239828 - cp's OEIS frontend

A160711 Cyclops squares: squares (A000290) that are also cyclops numbers (A134808).

0, 11025, 19044, 21025, 24025, 32041, 38025, 42025, 47089, 51076, 58081, 59049, 65025, 66049, 67081, 75076, 87025, 93025, 1110916, 1140624, 1170724, 1190281, 1240996, 1270129, 1290496, 1340964, 1350244, 1380625, 1420864, 1430416

Offset: 1

Omar E. Pol, Jun 08 2009

			19044 is in the sequence because it is a square (138^2) and is also a cyclops number (odd number of digits, middle digit is the only zero).
11025 is in the sequence because it is a square (105^2) and is also a cyclops number (odd number of digits, middle digit is the only zero). - _Michael B. Porter_, Jul 09 2016

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

Cf. A000290, A134808, A134809, A134148, A138131, A153806, A160712, A160717, A239828.

Select[Range[0, 1200]^2, And[OddQ@ Length@ #, #[[Ceiling[Length[#]/2]]] == 0, Count[#, 0] == 1] &@ IntegerDigits@ # &] (* Michael De Vlieger, Jul 08 2016 *)
cnQ[n_]:=Module[{len=IntegerLength[n]},OddQ[len]&&DigitCount[n,10,0]==1 && IntegerDigits[n][[(len+1)/2]]==0]; Join[{0},Select[Range[1200]^2,cnQ]] (* Harvey P. Dale, Mar 19 2018 *)

A239827 Cyclops numbers whose squares are cyclops numbers.

Original entry on oeis.org

0, 105, 205, 305, 11014, 11023, 11041, 11059, 12017, 12021, 12046, 12075, 12079, 13027, 13031, 13096, 14011, 14018, 14043, 14068, 14075, 14082, 16019, 16022, 16044, 16072, 16075, 17012, 17091, 17094, 18014, 18039, 18075, 18086, 19016, 19029, 19037, 19058

Offset: 1

Colin Barker, Mar 27 2014

Subsequence of A239589.

			12046 is in the sequence because 12046^2 = 145106116, and both 12406 and 145106116 are cyclops numbers.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A134808, A239589, A239828.

is_cyclops(k) = {
  if(k==0, return(1));
  my(d=digits(k), j);
  if(#d%2==0 || d[#d\2+1]!=0, return(0));
  for(j=1, #d\2, if(d[j]==0, return(0)));
  for(j=#d\2+2, #d, if(d[j]==0, return(0)));
  return(1)}
s=[]; for(n=0, 100000, if(is_cyclops(n) && is_cyclops(n^2), s=concat(s, n))); s

a(n) = sqrt(A239828(n)).

A286662 Numbers k such that k, k^2 and k^3 are cyclops numbers (A134808).

Original entry on oeis.org

0, 16075, 18039, 1130239, 1130363, 1130668, 1150474, 1220156, 1230423, 1250928, 1290628, 1330162, 1350478, 1390313, 1390989, 1510414, 1510712, 1530314, 1530461, 1530585, 1540896, 1540977, 1560186, 1560324, 1570341, 1580342, 1620244, 1620389, 1630871, 1650288

Offset: 1

Colin Barker, May 12 2017

For k = 1130239, k^4 = 1631853457220539336688641 is also a cyclops number.

			16075 is in the sequence because k^2 = 258405625, k^3 = 4153870421875 and these three numbers are cyclops numbers.

Cf. A000290, A000578, A134808, A160711, A239587, A239588, A239589, A239590, A239591, A239827, A239828.

cycQ[n_]:=DigitCount[n,10,0]==1&&OddQ[IntegerLength[n]]&& IntegerDigits[ n][[(IntegerLength[n]+1)/2]]==0; Join[{0},Table[Select[Range[ 10^n, 10^(n+1)-1],AllTrue[{#,#^2,#^3},cycQ]&],{n,2,6,2}]]//Flatten (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 25 2017 *)

is_cyclops(k) = {
  if(k==0, return(1));
  my(d=digits(k), j);
  if(#d%2==0 || d[#d\2+1]!=0, return(0));
  for(j=1, #d\2, if(d[j]==0, return(0)));
  for(j=#d\2+2, #d, if(d[j]==0, return(0)));
  return(1)}
L=List(); for(n=0, 10000000, if(is_cyclops(n) && is_cyclops(n^2) && is_cyclops(n^3), listput(L, n))); Vec(L)

cp's OEIS Frontend

A160711 Cyclops squares: squares (A000290) that are also cyclops numbers (A134808).

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A239827 Cyclops numbers whose squares are cyclops numbers.

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A286662 Numbers k such that k, k^2 and k^3 are cyclops numbers (A134808).

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