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.

A067479 Smallest n-digit square starting with 9, or 0 if no such number exists.

Original entry on oeis.org

9, 0, 900, 9025, 90000, 900601, 9000000, 90003169, 900000000, 9000127161, 90000000000, 900001331856, 9000000000000, 90000000369889, 900000000000000, 9000000036988900, 90000000000000000, 900000001801523401
Offset: 1

Views

Author

Amarnath Murthy, Feb 09 2002

Keywords

Crossrefs

Cf. A000290, A035076 (roots), A045792.
Cf. 2: A067472, 3: A067473, 4: A067474, 5: A067475, 6: A067476, 7: A067477, 8: A067478.

Programs

  • PARI
    a(n) = if (n==2, 0, (sqrtint(9*10^(n-1)) + (n-1) % 2)^2); \\ Michel Marcus, Mar 23 2021

Formula

a(n+1) = (floor(sqrt(9*10^n)) + (n mod 2))^2, a(2)=0. - Sascha Kurz, Mar 18 2002
a(2k+1) = 9 * 10^(2k) for k >= 0. - Bernard Schott, Mar 23 2021

Extensions

More terms from Sascha Kurz, Mar 18 2002

A035069 a(n) is root of square starting with digit 2: first term of runs.

Original entry on oeis.org

5, 15, 45, 142, 448, 1415, 4473, 14143, 44722, 141422, 447214, 1414214, 4472136, 14142136, 44721360, 141421357, 447213596, 1414213563, 4472135955, 14142135624, 44721359550, 141421356238, 447213595500, 1414213562374
Offset: 1

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Crossrefs

Cf. A067472 (squares), A035076 (2..9).

Programs

  • Mathematica
    Table[Ceiling @ Sqrt[2 * 10^n], {n, 1, 24}] (* Amiram Eldar, Oct 08 2019 *)

Formula

a(n) = ceiling(sqrt(2*10^n)).

Extensions

Offset 1 from Michel Marcus, Oct 08 2019

A035070 a(n) is root of square starting with digit 3: first term of runs.

Original entry on oeis.org

6, 18, 55, 174, 548, 1733, 5478, 17321, 54773, 173206, 547723, 1732051, 5477226, 17320509, 54772256, 173205081, 547722558, 1732050808, 5477225576, 17320508076, 54772255751, 173205080757, 547722557506, 1732050807569, 5477225575052, 17320508075689, 54772255750517
Offset: 1

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Links

Crossrefs

Cf. A067473 (squares), A035076 (2..9).

Programs

  • Mathematica
    Table[Ceiling @ Sqrt[3 * 10^n], {n, 1, 24}] (* Amiram Eldar, Oct 08 2019 *)
  • Python
    from math import isqrt
def a(n): return isqrt(3*10**n) + 1
print([a(n) for n in range(1, 28)]) # Michael S. Branicky, Jun 18 2021

Formula

a(n) = ceiling(sqrt(3*10^n)).

Extensions

Offset 1 from Alois P. Heinz, Oct 08 2019

A035073 a(n) is root of square starting with digit 6: first term of runs.

Original entry on oeis.org

8, 25, 78, 245, 775, 2450, 7746, 24495, 77460, 244949, 774597, 2449490, 7745967, 24494898, 77459667, 244948975, 774596670, 2449489743, 7745966693, 24494897428, 77459666925, 244948974279, 774596669242, 2449489742784, 7745966692415, 24494897427832, 77459666924149
Offset: 1

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Crossrefs

Subsequence of A045860.
Cf. A067576 (squares), A035076 (2..9).

Programs

  • Python
    from math import isqrt
def a(n): return isqrt(6*10**n) + 1
print([a(n) for n in range(1, 28)]) # Michael S. Branicky, Aug 25 2021

Formula

a(n) = ceiling(sqrt(6*10^n)), n > 0.

A035075 a(n) = ceiling(sqrt(8*10^n)).

Original entry on oeis.org

9, 29, 90, 283, 895, 2829, 8945, 28285, 89443, 282843, 894428, 2828428, 8944272, 28284272, 89442720, 282842713, 894427191, 2828427125, 8944271910, 28284271248, 89442719100, 282842712475, 894427191000, 2828427124747
Offset: 1

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Comments

Also, first term of runs of consecutive numbers whose square starts with the digit 8.

Crossrefs

Cf. A067478 (squares), A035069-A035076 (2..9), A045862.

Programs

  • Mathematica
    Ceiling[Sqrt[8*10^Range[30]]] (* Harvey P. Dale, Apr 12 2013 *)
  • Python
    from math import isqrt
def a(n): return isqrt(8*10**n) + 1
print([a(n) for n in range(1, 25)]) # Michael S. Branicky, Sep 29 2021

Formula

a(n) = ceiling(sqrt(8*10^n)), n > 0.

A035071 a(n) = ceiling(sqrt(4*10^n)).

Original entry on oeis.org

2, 7, 20, 64, 200, 633, 2000, 6325, 20000, 63246, 200000, 632456, 2000000, 6324556, 20000000, 63245554, 200000000, 632455533, 2000000000, 6324555321, 20000000000, 63245553204, 200000000000, 632455532034, 2000000000000
Offset: 0

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Comments

Previous name: "a(n) is root of square starting with digit 4: first term of runs."

Crossrefs

Cf. A067474 (squares), A035076 (2..9).

Programs

  • Mathematica
    Table[Ceiling @ Sqrt[4 * 10^n], {n, 0, 24}] (* Amiram Eldar, Oct 08 2019 *)

A035072 a(n) is root of square starting with digit 5: first term of runs.

Original entry on oeis.org

23, 71, 224, 708, 2237, 7072, 22361, 70711, 223607, 707107, 2236068, 7071068, 22360680, 70710679, 223606798, 707106782, 2236067978, 7071067812, 22360679775, 70710678119, 223606797750, 707106781187, 2236067977500
Offset: 2

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Crossrefs

Cf. A067475 (squares), A035076 (2..9).

Programs

  • Mathematica
    Table[Ceiling @ Sqrt[5 * 10^n], {n, 2 , 24}] (* Amiram Eldar, Oct 08 2019 *)

Formula

a(n) = ceiling(sqrt(5*10^n)), n > 1.

A035074 a(n) is root of square starting with digit 7: first term of runs.

Original entry on oeis.org

27, 84, 265, 837, 2646, 8367, 26458, 83667, 264576, 836661, 2645752, 8366601, 26457514, 83666003, 264575132, 836660027, 2645751312, 8366600266, 26457513111, 83666002654, 264575131107, 836660026535, 2645751311065
Offset: 2

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Crossrefs

Cf. A067477 (squares), A035076 (2..9).

Programs

  • Mathematica
    Ceiling[Sqrt[7*10^Range[2,30]]] (* Harvey P. Dale, Jan 21 2015 *)

Formula

a(n) = ceiling(sqrt(7*10^n)), n > 1.
Showing 1-8 of 8 results.

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