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 1-10 of 23 results. Next

A279420 Numbers k such that k^2 has an odd number of digits and the middle digit is 0.

Original entry on oeis.org

10, 20, 30, 100, 105, 138, 145, 155, 179, 195, 200, 205, 217, 226, 241, 243, 245, 247, 249, 251, 253, 255, 257, 259, 274, 283, 295, 300, 305, 1000, 1005, 1010, 1015, 1020, 1025, 1030, 1049, 1054, 1068, 1082, 1091, 1100, 1114, 1127, 1136, 1149, 1158, 1162, 1175
Offset: 1

Views

Author

Lars Blomberg, Dec 12 2016

Keywords

Examples

			10^2 = 1(0)0, 195^2 = 38(0)25, 1000^2 = 100(0)000.
The sequences of squares starts: 100, 400, 900, 10000, 11025, 19044, 21025, 24025, 32041, 38025, 40000, ...

Links

Crossrefs

Cf. A279421-A279429.

Programs

  • Mathematica
    Select[Range@ 1175, Function[w, And[OddQ@ Length@ w, First@ Take[w, {Ceiling[Length[w]/2]}] == 0]]@ IntegerDigits[#^2] &] (* Michael De Vlieger, Dec 12 2016 *)
Select[Range[1200],With[{len=IntegerLength[#^2]},OddQ[len]&&IntegerDigits[#^2][[(len+1)/2]]==0&]] (* Harvey P. Dale, Mar 29 2025 *)
  • PARI
    isok(n) = my(d=digits(n^2)); (#d % 2) && (d[#d\2 + 1] == 0); \\ Michel Marcus, Dec 18 2016

A279430 Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 0.

Original entry on oeis.org

0, 2, 4, 5, 8, 9, 10, 16, 17, 18, 19, 22, 32, 33, 34, 35, 36, 37, 40, 41, 44, 64, 65, 66, 67, 68, 69, 70, 71, 76, 77, 80, 81, 84, 85, 87, 90, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 145, 146, 147, 151, 152, 153, 156, 157, 160, 161, 164
Offset: 1

Views

Author

Lars Blomberg, Jan 07 2017

Keywords

Links

Crossrefs

Cf. A279431.
See A279420-A279429 for a base-10 version.

Programs

  • Mathematica
    a[n_]:=Part[IntegerDigits[n,2],(Length[IntegerDigits[n,2]]+1)/2];
Select[Range[0,164],OddQ[Length[IntegerDigits[#^2,2]]] && a[#^2]==0 &] (* Indranil Ghosh, Mar 06 2017 *)
k2oQ[n_]:=Module[{idn=IntegerDigits[n^2,2],len},len=Length[idn];OddQ[ len] && idn[[(len+1)/2]]==0]; Select[Range[0,200],k2oQ] (* Harvey P. Dale, Jan 29 2020 *)
  • PARI
    isok(k) = my(d=digits(k^2, 2)); (#d%2 == 1) && (d[#d\2 +1] == 0);
for(k=0, 164, if(k==0 || isok(k)==1, print1(k,", "))); \\ Indranil Ghosh, Mar 06 2017
  • Python
    i=0
j=1
while i<=164:
    n=str(bin(i**2)[2:])
    l=len(n)
    if l%2 and n[(l-1)//2]=="0":
        print(str(i), end=",")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A279431 Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 1.

Original entry on oeis.org

1, 11, 20, 21, 38, 39, 42, 43, 45, 72, 73, 74, 75, 78, 79, 82, 83, 86, 88, 89, 140, 141, 142, 143, 148, 149, 150, 154, 155, 158, 159, 162, 163, 166, 167, 169, 170, 172, 173, 175, 178, 180, 181, 272, 273, 274, 275, 276, 277, 278, 284, 285, 286, 287, 292, 293
Offset: 1

Views

Author

Lars Blomberg, Jan 07 2017

Keywords

Examples

			1^2 = (1), 72^2 = 101000(1)000000, 158^2 = 1100001(1)0000100

Links

Crossrefs

Cf. A279430.
See A279420-A279429 for a base 10 version.

Programs

  • Mathematica
    a[n_]:=Part[IntegerDigits[n, 2], (Length[IntegerDigits[n, 2]] + 1)/2];
Select[Range[0, 293], OddQ[Length[IntegerDigits[#^2, 2]]] && a[#^2]==1 &] (* Indranil Ghosh, Mar 06 2017 *)
  • PARI
    isok(k) = my(d=digits(k^2, 2)); (#d%2 == 1) && (d[#d\2 +1] == 1);
for(k=0, 293, if(isok(k)==1, print1(k,", "))); \\ Indranil Ghosh, Mar 06 2017
  • Python
    i=0
j=1
while i<=293:
    n=str(bin(i**2)[2:])
    l=len(n)
    if l%2 and n[(l-1)//2]=="1":
        print(str(i), end=",")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A280640 Numbers k such that k^3 has an odd number of digits and the middle digit is 0.

Original entry on oeis.org

0, 30, 40, 42, 100, 101, 115, 116, 123, 126, 135, 163, 164, 171, 199, 200, 201, 214, 468, 479, 487, 498, 500, 502, 513, 520, 525, 543, 557, 562, 564, 575, 576, 577, 578, 579, 585, 596, 600, 615, 623, 642, 656, 661, 666, 690, 695, 697, 700, 705, 709, 717, 721
Offset: 1

Views

Author

Lars Blomberg, Jan 07 2017

Keywords

Comments

The sequence of cubes starts: 0, 27000, 64000, 74088, 1000000, 1030301, 1520875, 1560896, ...

Examples

			0^3 = (0), 126^3 = 200(0)376, 562^3 = 1775(0)4328.

Links

Crossrefs

Cf. A280641-A280649, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

Programs

  • Mathematica
    a[n_]:=Part[IntegerDigits[n], (Length[IntegerDigits[n]] + 1)/2];
Select[Range[0, 721], OddQ[Length[IntegerDigits[#^3]]] && a[#^3]==0 &] (* Indranil Ghosh, Mar 06 2017 *)
  • PARI
    isok(k) = my(d=digits(k^3)); (#d%2 == 1) && (d[#d\2 +1] == 0);
for(k=0, 721, if(k==0 || isok(k)==1, print1(k, ", "))); \\ Indranil Ghosh, Mar 06 2017
  • Python
    i=0
j=1
while i<=721:
    n=str(i**3)
    l=len(n)
    if l%2 and n[(l-1)//2]=="0":
        print(str(i), end=",")
        j+=1
    i+=1 # Indranil Ghosh, Mar 06 2017

A280649 Numbers k such that k^3 has an odd number of digits and the middle digit is 9.

Original entry on oeis.org

28, 33, 41, 108, 132, 157, 159, 175, 178, 181, 184, 187, 190, 193, 196, 204, 207, 209, 466, 474, 480, 486, 492, 508, 514, 515, 518, 519, 528, 536, 539, 552, 570, 588, 611, 627, 638, 648, 651, 657, 658, 659, 660, 706, 707, 708, 714, 719, 745, 757, 763, 765, 772
Offset: 1

Views

Author

Lars Blomberg, Jan 07 2017

Keywords

Comments

The sequence of cubes starts: 21952, 35937, 68921, 1259712, 2299968, 3869893, 4019679, 5359375, ...

Examples

			28^3 = 21(9)52, 181^3 = 592(9)741, 536^3 = 1539(9)0656.

Links

Crossrefs

Cf. A280640-A280648, A181354.
See A279420-A279429 for a k^2 version.
See A279430-A279431 for a k^2 version in base 2.

Programs

  • Mathematica
    ond9Q[n_]:=Module[{idn=IntegerDigits[n^3],len},len=Length[idn];OddQ[len]&&idn[[(len+1)/2]]==9]; Select[Range[800],ond9Q] (* Harvey P. Dale, Mar 14 2018 *)

A279421 Numbers k such that k^2 has an odd number of digits and the middle digit is 1.

Original entry on oeis.org

1, 110, 119, 123, 127, 131, 142, 152, 182, 190, 210, 224, 237, 239, 261, 263, 276, 290, 310, 1035, 1040, 1059, 1073, 1087, 1096, 1105, 1123, 1132, 1141, 1145, 1154, 1167, 1171, 1184, 1188, 1209, 1213, 1217, 1285, 1289, 1293, 1312, 1316, 1331, 1346, 1357, 1368
Offset: 1

Views

Author

Lars Blomberg, Dec 22 2016

Keywords

Examples

			1^2 = (1), 190^2 = 36(1)00, 1145^2 = 131(1)025.

Links

Crossrefs

Cf. A279420, A279422-A279429.

Programs

  • Mathematica
    ond1Q[n_]:=Module[{len=IntegerLength[n^2]},OddQ[len]&&IntegerDigits[n^2][[(len+1)/2]]==1]; Select[Range[1500],ond1Q] (* Harvey P. Dale, Jun 06 2018 *)

A279422 Numbers k such that k^2 has an odd number of digits and the middle digit is 2.

Original entry on oeis.org

11, 15, 18, 23, 25, 27, 101, 106, 115, 135, 149, 159, 162, 165, 168, 171, 174, 185, 193, 198, 203, 208, 215, 222, 233, 235, 265, 267, 278, 285, 292, 297, 302, 307, 315, 1001, 1006, 1011, 1016, 1021, 1026, 1031, 1045, 1050, 1064, 1069, 1078, 1083, 1092, 1101
Offset: 1

Views

Author

Lars Blomberg, Dec 22 2016

Keywords

Examples

			11^2 = 1(2)1, 135^2 = 18(2)25, 285^2 = 81(2)25.

Links

Crossrefs

Cf. A279420-A279421, A279423-A279429.

Programs

  • Mathematica
    Select[Range[1101], OddQ[len=Length[IntegerDigits[#^2]]]&&Part[IntegerDigits[#^2], (len+1)/2]==2 &] (* Stefano Spezia, Oct 03 2023 *)

A279423 Numbers k such that k^2 has an odd number of digits and the middle digit is 3.

Original entry on oeis.org

111, 124, 128, 139, 146, 156, 177, 188, 213, 231, 269, 287, 312, 1036, 1041, 1055, 1060, 1074, 1088, 1097, 1106, 1115, 1124, 1133, 1146, 1159, 1172, 1189, 1193, 1214, 1218, 1222, 1226, 1274, 1278, 1282, 1286, 1305, 1309, 1313, 1328, 1343, 1354, 1365, 1376
Offset: 1

Views

Author

Lars Blomberg, Dec 22 2016

Keywords

Examples

			111^2 = 12(3)21, 231^2 = 53(3)61, 1214^2 = 147(3)796.

Links

Crossrefs

Cf. A279420-A279422, A279424-A279429.

Programs

  • Mathematica
    ond3Q[n_]:=Module[{idn2=IntegerDigits[n^2],len},len=Length[idn2];OddQ[ len] && idn2[[(len+1)/2]]==3]; Select[Range[1400],ond3Q] (* Harvey P. Dale, Apr 06 2018 *)

A279424 Numbers k such that k^2 has an odd number of digits and the middle digit is 4.

Original entry on oeis.org

2, 12, 21, 29, 102, 107, 116, 120, 132, 136, 143, 153, 180, 183, 191, 196, 201, 206, 220, 229, 271, 280, 294, 299, 304, 309, 1002, 1007, 1012, 1017, 1022, 1027, 1046, 1051, 1065, 1070, 1079, 1093, 1102, 1111, 1120, 1129, 1142, 1151, 1155, 1164, 1168, 1181
Offset: 1

Views

Author

Lars Blomberg, Dec 22 2016

Keywords

Examples

			2^2 = (4), 136^2 = 18(4)96, 1017^2 = 103(4)289.

Links

Crossrefs

Cf. A279420-A279423, A279425-A279429.

Programs

  • Mathematica
    Select[Range[1200],OddQ[IntegerLength[#^2]]&&IntegerDigits[#^2][[(IntegerLength[ #^2]+1)/2]]==4&] (* Harvey P. Dale, Jun 05 2017 *)

A279425 Numbers k such that k^2 has an odd number of digits and the middle digit is 5.

Original entry on oeis.org

16, 112, 150, 163, 166, 169, 172, 186, 211, 218, 227, 242, 244, 246, 248, 250, 252, 254, 256, 258, 273, 282, 289, 314, 1032, 1037, 1042, 1056, 1061, 1075, 1084, 1089, 1098, 1107, 1116, 1125, 1134, 1138, 1147, 1160, 1173, 1177, 1194, 1198, 1219, 1223, 1227
Offset: 1

Views

Author

Lars Blomberg, Dec 22 2016

Keywords

Examples

			16^2 = 2(5)6, 218^2 = 47(5)24, 1075^2 = 115(5)625.

Links

Crossrefs

Cf. A279420-A279424, A279426-A279429.

Programs

  • Mathematica
    Select[Range[1227], OddQ[len=Length[IntegerDigits[#^2]]]&&Part[IntegerDigits[#^2], (len+1)/2]==5 &] (* Stefano Spezia, Oct 03 2023 *)
Showing 1-10 of 23 results. Next

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