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 1-3 of 3 results.

A053973 Squares composed of digits {6,7,9}.

Original entry on oeis.org

9, 676, 69696, 97969, 9696996, 9697699776769, 77797697969777769, 776797677679677696, 6776696769676669969, 9767769967769766976, 97667999767779769677969, 7676999976999997667777796, 69997676676669667699797969, 67976976676979976697777676769, 96667776776767999797799699976676
Offset: 1

Views

Author

Patrick De Geest, Mar 15 2000

Keywords

Crossrefs

Cf. A053972.

Programs

  • Mathematica
    Flatten[Table[Select[FromDigits/@Tuples[{6,7,9},i],IntegerQ[Sqrt[#]]&],{i,23}]] (* Harvey P. Dale, Dec 07 2014 *)

Formula

a(n) = A053972(n)^2.

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 14 2005
a(12)-a(15) from Mishima's website, added by Max Alekseyev, Nov 30 2017

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

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

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 1-3 of 3 results.