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 1-8 of 8 results.

A291626 Numbers k such that 1 is the smallest decimal digit of k^2.

Original entry on oeis.org

1, 4, 9, 11, 12, 13, 14, 19, 21, 29, 31, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 54, 56, 59, 61, 69, 72, 79, 81, 89, 91, 96, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134
Offset: 1

Views

Author

Colin Barker, Aug 28 2017

Keywords

Examples

			29 is in the sequence because 29^2 = 841, the smallest decimal digit of which is 1.

Links

Crossrefs

Cf. A291625, A291627, A291628, A291629, A291630, A291631.

Programs

  • Mathematica
    Select[Range[200],Min[IntegerDigits[#^2]]==1&] (* Harvey P. Dale, Sep 07 2019 *)
  • PARI
    select(k->vecmin(digits(k^2))==1, vector(1000, k, k))
  • Python
    A291626_list = [k for k in range(1,10**6) if min(str(k**2)) == '1'] # Chai Wah Wu, Aug 28 2017

A291628 Numbers k such that 3 is the smallest decimal digit of k^2.

Original entry on oeis.org

6, 58, 62, 63, 66, 86, 94, 183, 184, 186, 187, 188, 192, 194, 213, 244, 256, 272, 294, 306, 312, 583, 586, 587, 588, 607, 608, 612, 613, 614, 616, 622, 624, 628, 663, 666, 688, 706, 734, 744, 764, 806, 812, 833, 857, 874, 876, 913, 914, 924, 942, 1833, 1834
Offset: 1

Views

Author

Colin Barker, Aug 28 2017

Keywords

Examples

			58 is in the sequence because 58^2 = 3364, the smallest decimal digit of which is 3.

Links

Crossrefs

Cf. A291625, A291626, A291627, A291629, A291630, A291631.

Programs

  • Mathematica
    Select[Range[10^4], Min[IntegerDigits[#^2]]==3 &] (* Vincenzo Librandi, Sep 10 2017 *)
  • PARI
    select(k->vecmin(digits(k^2))==3, vector(2000, k, k))

A291629 Numbers k such that 4 is the smallest decimal digit of k^2.

Original entry on oeis.org

2, 7, 8, 22, 28, 67, 74, 88, 92, 93, 212, 214, 216, 234, 238, 242, 258, 262, 293, 308, 667, 676, 678, 683, 684, 692, 707, 738, 758, 772, 817, 822, 828, 863, 864, 866, 886, 888, 892, 893, 926, 938, 972, 974, 978, 2113, 2114, 2116, 2133, 2137, 2158, 2163, 2167
Offset: 1

Views

Author

Colin Barker, Aug 28 2017

Keywords

Comments

First digit can't be 1, 4 or 5; last digit can't be 0, 1 or 9. - Robert Israel, Mar 25 2020

Examples

			28 is in the sequence because 28^2 = 784, the smallest decimal digit of which is 4.

Links

Crossrefs

Cf. A291625, A291626, A291627, A291628, A291630, A291631.

Programs

  • Maple
    filter:= n -> min(convert(n^2,base,10))=4:
select(filter, [$1..10000]); # Robert Israel, Mar 25 2020
  • Mathematica
    Select[Range[2500],Min[IntegerDigits[#^2]]==4&] (* Harvey P. Dale, Aug 03 2019 *)
  • PARI
    select(k->vecmin(digits(k^2))==4, vector(3000, k, k))

A291630 Numbers k such that 5 is the smallest decimal digit of k^2.

Original entry on oeis.org

24, 76, 87, 236, 314, 316, 766, 816, 834, 2366, 2383, 2387, 2424, 2563, 2626, 2976, 7613, 7666, 8117, 8184, 8234, 8286, 8366, 8716, 8814, 9266, 9316, 9363, 9474, 9786, 9837, 23634, 23784, 23866, 23874, 24474, 25663, 25684, 26076, 26187, 26374, 26417, 27687
Offset: 1

Views

Author

Colin Barker, Aug 28 2017

Keywords

Examples

			87 is in the sequence because 87^2 = 7569, the smallest decimal digit of which is 5.

Links

Crossrefs

Cf. A291625, A291626, A291627, A291628, A291629, A291631.

Programs

  • Mathematica
    Select[Range[30000],Min[IntegerDigits[#^2]]==5&] (* Harvey P. Dale, Nov 03 2023 *)
  • PARI
    select(k->vecmin(digits(k^2))==5, vector(30000, k, k))
  • Python
    A291630_list = [k for k in range(1,10**6) if min(str(k**2)) == '5'] # Chai Wah Wu, Aug 28 2017

A291625 Numbers k such that 0 is the smallest decimal digit of k^2.

Original entry on oeis.org

10, 20, 30, 32, 33, 40, 45, 47, 48, 49, 50, 51, 52, 53, 55, 60, 64, 70, 71, 78, 80, 84, 90, 95, 97, 98, 99, 100, 101, 102, 103, 104, 105, 110, 120, 130, 138, 140, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 155, 160, 170, 174, 175, 176, 179, 180
Offset: 1

Views

Author

Colin Barker, Aug 28 2017

Keywords

Examples

			47 is in the sequence because 47^2 = 2209, the smallest decimal digit of which is 0.

Crossrefs

Cf. A291626, A291627, A291628, A291629, A291630, A291631.

Programs

  • PARI
    select(k->vecmin(digits(k^2))==0, vector(1000, k, k))
  • Python
    A291625_list = [k for k in range(1,10**6) if '0' in str(k**2)] # Chai Wah Wu, Aug 28 2017

A291627 Numbers k such that 2 is the smallest decimal digit of k^2.

Original entry on oeis.org

5, 15, 16, 17, 18, 23, 25, 27, 57, 65, 68, 73, 75, 77, 82, 85, 156, 157, 158, 162, 163, 164, 165, 166, 167, 168, 172, 173, 185, 193, 206, 207, 208, 215, 218, 222, 223, 232, 233, 235, 273, 275, 277, 278, 282, 287, 288, 292, 307, 315, 472, 473, 474, 475, 476
Offset: 1

Views

Author

Colin Barker, Aug 28 2017

Keywords

Examples

			278 is in the sequence because 278^2 = 77284, the smallest decimal digit of which is 2.

Crossrefs

Cf. A291625, A291626, A291628, A291629, A291630, A291631.

Programs

  • PARI
    select(k->vecmin(digits(k^2))==2, vector(1000, k, k))

A379602 a(n) is the least n-digit number whose square contains only digits greater than 5.

Original entry on oeis.org

3, 26, 264, 3114, 25824, 260167, 2639867, 25845676, 260147437, 2582245083, 25843178924, 258241744863, 2582010592114, 25825761924437, 258218875510676, 2581990857627114, 25820083014911063, 258199298347206526, 2581988959445543367, 25819892911624938937, 258198891881411585714
Offset: 1

Views

Author

Zhining Yang, Dec 27 2024

Keywords

Comments

Exists for all n because A379603(n) does (see Formulas there). - Michael S. Branicky, Dec 30 2024

Examples

			a(3) = 264 because among all 3-digit numbers, 264 is the smallest whose square 69696 contains only digits greater than 5.

Crossrefs

Cf. A053972, A053974, A058471, A164778, A164772, A164773, A164841, A291631, A379603.

Programs

  • Mathematica
    f[m_] := For[k = Ceiling@Sqrt[100^m/15], k < 10^m - 1, k++, If[Min@IntegerDigits[k^2] > 5, Return[k];]]; Table[f[m], {m, 10}]

Extensions

a(9) corrected and a(11) inserted by Michael S. Branicky, Dec 27 2024
More terms from Jinyuan Wang, Dec 27 2024

A379603 a(n) is the largest n-digit number whose square contains only digits greater than 5.

Original entry on oeis.org

3, 83, 937, 9833, 98336, 998333, 9994833, 99983333, 999939437, 9999833333, 99998333336, 999998333333, 9999983333336, 99999983333333, 999999833333336, 9999999833333333, 99999998333333336, 999999998333333333, 9999999983333333336, 99999999983333333333, 999999999833333333336
Offset: 1

Views

Author

Zhining Yang, Dec 27 2024

Keywords

Examples

			a(3) = 937 because among all 3-digit numbers, 937 is the largest whose square 877969 contains only digits greater than 5.

Crossrefs

Cf. A053972, A053974, A058471, A164778, A164772, A164773, A164841, A291631, A379602.

Programs

  • Mathematica
    f[m_] := For[k = 10^m - 1, k > 10^(m - 1), k--, If[Min@IntegerDigits[k^2] > 5, Return[k];]];
Table[f[m], {m, 10}]

Formula

Conjecture: It appears that for all n >= 5,
a(2*n) = 100^n - (5*10^n + 1)/3, and
a(2*n + 1) = 10*a(2*n) + 6.

Extensions

a(20)-a(21) from Jinyuan Wang, Dec 27 2024
Showing 1-8 of 8 results.

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