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 1-4 of 4 results.

A077431 n repeated in decimal representation, but separated by enough zeros that the square has the pattern (n^2)(2n^2)(n^2).

Original entry on oeis.org

11, 22, 303, 404, 505, 606, 707, 8008, 9009, 10010, 11011, 12012, 13013, 14014, 15015, 16016, 17017, 18018, 19019, 20020, 21021, 22022, 230023, 240024, 250025, 260026, 270027, 280028, 290029, 300030, 310031, 320032, 330033, 340034, 350035
Offset: 1

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Author

Reinhard Zumkeller, Nov 05 2002

Keywords

Comments

A077433(n) = number of separating zeros.

Examples

			a(17) = 17017, as 17017^2 = 289578289 = A077432(17) = 289'578'289 and 289=17^2 and 578=2*289.

Crossrefs

Cf. A020338, A004216, A077430.

Programs

  • Mathematica
    a[n_] := For[idn = IntegerDigits[n]; k = 0, True, k++, an = FromDigits[ Join[idn, Table[0, k], idn]]; If[MatchQ[IntegerDigits[an^2], {b__ /; IntegerQ[Sqrt[FromDigits[{b}]]], c___, 0..., b__} /; FromDigits[{c}] == 2*FromDigits[{b}]], Return[an]]];
Array[a, 35] (* Jean-François Alcover, Nov 13 2017 *)

Formula

a(n) = n*(1+10^(1+floor(log_10(2*n^2)))).

A077432 Squares of the form u'v'w, where in decimal representation u=n^2, v=2*n^2 and w=n^2 possibly with a leading zero.

Original entry on oeis.org

121, 484, 91809, 163216, 255025, 367236, 499849, 64128064, 81162081, 100200100, 121242121, 144288144, 169338169, 196392196, 225450225, 256512256, 289578289, 324648324, 361722361, 400800400, 441882441, 484968484, 52910580529
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 05 2002

Keywords

Comments

a(n) = A077431(n)^2.

Examples

			n=42, n^2=1764 and 2*n^2=3528: a(42) = 1764'3528'1764 = 420042^2 = A077431(42)^2.

Crossrefs

Cf. A004216, A077430, A077431.

Formula

a(n) = (n*(1 + 10^(1 + floor(log_10(2*n^2)))))^2.

A077433 Number of separating zeros to represent A077431.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 05 2002

Keywords

Examples

			a(256)=3, as A077431(256)=256000256 and A077432(256)=256000256^2=65536'131072'065536; two zeros would not be enough, as 25600256^2 = 65537'31072'65536.

Crossrefs

a(n) = floor(A077430(n)/2).

Formula

a(n) = floor((floor(log_10(2*n^2))+1)/2).

A077429 a(n) = floor(log_10(n^2)).

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 05 2002

Keywords

Comments

a(n) = A004216(n^2).

Crossrefs

Cf. A004216, A077430.

Programs

  • Mathematica
    Table[Floor[Log10[n^2]],{n,120}] (* Harvey P. Dale, Sep 17 2020 *)
Showing 1-4 of 4 results.

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