cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A239589 Numbers whose squares are cyclops numbers.

Original entry on oeis.org

0, 105, 138, 145, 155, 179, 195, 205, 217, 226, 241, 243, 255, 257, 259, 274, 295, 305, 1054, 1068, 1082, 1091, 1114, 1127, 1136, 1158, 1162, 1175, 1192, 1196, 1221, 1229, 1233, 1237, 1261, 1269, 1273, 1277, 1281, 1308, 1323, 1327, 1338, 1364, 1375, 1386
Offset: 1

Views

Author

Colin Barker, Mar 24 2014

Keywords

Examples

			138 is in the sequence because 138^2 = 19044, which is a cyclops number.

Links

Crossrefs

Cf. A000290, A134808, A160711, A239587, A239588, A239590, A239591.

Programs

  • PARI
    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, 2000, if(is_cyclops(n^2), s=concat(s, n))); s

A239587 Cubes that are cyclops numbers.

Original entry on oeis.org

0, 74088, 1520875, 1560896, 1860867, 2460375, 4330747, 4410944, 7880599, 123505992, 144703125, 172808693, 177504328, 179406144, 191102976, 194104539, 211708736, 232608375, 241804367, 264609288, 288804781, 295408296, 335702375, 338608873, 368601813, 374805361
Offset: 1

Views

Author

Colin Barker, Mar 24 2014

Keywords

Comments

Intersection of A000578 (Cubes) and A134808 (Cyclops numbers).

Links

Crossrefs

Cf. A000578, A134808, A160711, A239588, A239589, A239590, A239591.

Programs

  • Mathematica
    cyclpsQ[n_]:=With[{len=IntegerLength[n]},OddQ[len]&&DigitCount[n,10,0]==1&&IntegerDigits[n][[(len+1)/2]]==0]; Join[{0},Select[ Range[ 800]^3,cyclpsQ]] (* Harvey P. Dale, Nov 05 2024 *)
  • PARI
    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, 2000, if(is_cyclops(n^3), s=concat(s, n^3))); s

Formula

a(n) = A239590(n)^3.

A239588 Fourth powers that are cyclops numbers.

Original entry on oeis.org

0, 7890481, 9150625, 623201296, 981506241, 17363069361, 18945044881, 28813025536, 33871089681, 38167092496, 45954068161, 89526025681, 95565066496, 1421970391296, 1551160647936, 1736870953216, 3941340648961, 4771970346256, 5281980641536, 5436960129441
Offset: 1

Views

Author

Colin Barker, Mar 24 2014

Keywords

Comments

Intersection of A000583 (Fourth powers) and A134808 (Cyclops numbers).

Links

Crossrefs

Cf. A000583, A134808, A160711, A239587, A239589, A239590, A239591.

Programs

  • Mathematica
    cn4Q[n_]:=Module[{idn=IntegerDigits[n],len},len=Length[idn]; OddQ[ len] && idn[[(len+1)/2]]==0&&DigitCount[n,10,0]==1]; Select[Range[0,2000]^4, cn4Q] (* Harvey P. Dale, Dec 20 2015 *)
  • PARI
    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, 2000, if(is_cyclops(n^4), s=concat(s, n^4))); s

Formula

a(n) = A239591(n)^4.

A239591 Numbers whose fourth powers are cyclops numbers.

Original entry on oeis.org

0, 53, 55, 158, 177, 363, 371, 412, 429, 442, 463, 547, 556, 1092, 1116, 1148, 1409, 1478, 1516, 1527, 1612, 1622, 1633, 1692, 1694, 1724, 1738, 1754, 3262, 3263, 3276, 3283, 3338, 3362, 3366, 3402, 3436, 3464, 3468, 3473, 3512, 3538, 3631, 3723, 3724, 3833
Offset: 1

Views

Author

Colin Barker, Mar 24 2014

Keywords

Examples

			158 is in the sequence because 158^4 = 623201296, which is a cyclops number.

Links

Crossrefs

Cf. A000583, A134808, A160711, A239587, A239588, A239589, A239590.

Programs

  • PARI
    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, 5000, if(is_cyclops(n^4), s=concat(s, n))); s

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

Views

Author

Colin Barker, May 12 2017

Keywords

Comments

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

Examples

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

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • PARI
    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)
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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