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 10 results.

A045784 Squares with initial digit '1'.

Original entry on oeis.org

1, 16, 100, 121, 144, 169, 196, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 10000, 10201, 10404, 10609, 10816, 11025, 11236, 11449, 11664, 11881, 12100, 12321, 12544, 12769, 12996, 13225, 13456, 13689, 13924
Offset: 1

Views

Author

Jeff Burch

Keywords

Links

Crossrefs

Cf. A045855.
Cf. A045785, A045786, A045787, A045788, A045789, A045791, A045792, A045793.

Programs

  • Mathematica
    Select[Range[120]^2,First[IntegerDigits[#]]==1&] (* Harvey P. Dale, Dec 31 2011 *)

Formula

a(n) = A045855(n)^2. - Michel Marcus, Sep 04 2021

A045788 Squares with initial digit '5'.

Original entry on oeis.org

529, 576, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 50176, 50625, 51076, 51529, 51984, 52441, 52900, 53361, 53824, 54289, 54756, 55225, 55696, 56169, 56644, 57121, 57600, 58081, 58564, 59049, 59536, 501264, 502681, 504100, 505521
Offset: 1

Views

Author

Jeff Burch

Keywords

Links

Crossrefs

Cf. A045784, A045785, A045786, A045787, A045789, A045791, A045792, A045793.

Programs

  • Maple
    seq(op(map(`^`, [seq(i,i=ceil(sqrt(5*10^d))..floor(sqrt(6*10^d-1)))],2)),d=1..5); # Robert Israel, Sep 30 2016
  • Mathematica
    Flatten[Table[Range[Ceiling[Sqrt[5 10^n]],Floor[Sqrt[6 10^n]]]^2,{n,5}]]  (* Harvey P. Dale, Jun 15 2011 *)

Formula

a(n) = A045859(n)^2. - R. J. Mathar, Jul 23 2025

Extensions

Offset changed by Robert Israel, Sep 30 2016

A045789 Squares with initial digit '6'.

Original entry on oeis.org

64, 625, 676, 6084, 6241, 6400, 6561, 6724, 6889, 60025, 60516, 61009, 61504, 62001, 62500, 63001, 63504, 64009, 64516, 65025, 65536, 66049, 66564, 67081, 67600, 68121, 68644, 69169, 69696, 600625, 602176, 603729, 605284, 606841
Offset: 1

Views

Author

Jeff Burch

Keywords

Crossrefs

Cf. A045860.
Cf. A045784, A045785, A045786, A045787, A045788, A045791, A045792, A045793.

Programs

  • Mathematica
    Flatten[Table[Range[Ceiling[Sqrt[6 10^n]],Floor[Sqrt[7 10^n]]]^2,{n,5}]] (* Harvey P. Dale, Jun 15 2011 *)

Formula

a(n) = A045860(n)^2. - Michel Marcus, Sep 04 2021

A045787 Squares with initial digit '4'.

Original entry on oeis.org

4, 49, 400, 441, 484, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 40000, 40401, 40804, 41209, 41616, 42025, 42436, 42849, 43264, 43681, 44100, 44521, 44944, 45369, 45796, 46225, 46656, 47089, 47524, 47961, 48400, 48841, 49284, 49729, 400689
Offset: 1

Views

Author

Jeff Burch

Keywords

Crossrefs

Cf. A045858.
Cf. A045784, A045785, A045786, A045788, A045789, A045791, A045792, A045793.

Programs

  • Mathematica
    Flatten[Table[Range[Ceiling[Sqrt[4 10^n]],Floor[Sqrt[5 10^n]]]^2, {n,5}]] (* Harvey P. Dale, Jun 15 2011 *)

Formula

a(n) = A045858(n)^2. - Michel Marcus, Sep 04 2021

A045785 Squares with initial digit '2'.

Original entry on oeis.org

25, 225, 256, 289, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 20164, 20449, 20736, 21025, 21316, 21609, 21904, 22201, 22500, 22801, 23104, 23409, 23716, 24025, 24336, 24649, 24964, 25281, 25600, 25921, 26244, 26569
Offset: 1

Views

Author

Jeff Burch

Keywords

Crossrefs

Cf. A045856.
Cf. A045784, A045786, A045787, A045788, A045789, A045791, A045792, A045793.

Programs

  • Mathematica
    Flatten[Table[Range[Ceiling[Sqrt[2 10^n]],Floor[Sqrt[3 10^n]]]^2,{n,4}]](* Harvey P. Dale, Jun 15 2011 *)

Formula

a(n) = A045856(n)^2. - Michel Marcus, Sep 04 2021

A045786 Squares with initial digit '3'.

Original entry on oeis.org

36, 324, 361, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969, 30276, 30625, 30976, 31329, 31684, 32041, 32400, 32761, 33124, 33489, 33856, 34225, 34596, 34969, 35344, 35721, 36100, 36481, 36864, 37249, 37636, 38025, 38416, 38809
Offset: 1

Views

Author

Jeff Burch

Keywords

Crossrefs

Cf. A045857.
Cf. A045784, A045785, A045787, A045788, A045789, A045791, A045792, A045793.

Programs

  • Mathematica
    Select[Range[200]^2,First[IntegerDigits[#]]==3&]  (* Harvey P. Dale, Apr 21 2011 *)

Formula

a(n) = A045857(n)^2. - Michel Marcus, Sep 04 2021

A045791 Squares with initial digit '7'.

Original entry on oeis.org

729, 784, 7056, 7225, 7396, 7569, 7744, 7921, 70225, 70756, 71289, 71824, 72361, 72900, 73441, 73984, 74529, 75076, 75625, 76176, 76729, 77284, 77841, 78400, 78961, 79524, 700569, 702244, 703921, 705600, 707281, 708964, 710649, 712336
Offset: 1

Views

Author

Jeff Burch

Keywords

Crossrefs

Cf. A045861.
Cf. A045784, A045785, A045786, A045787, A045788, A045789, A045792, A045793.

Programs

  • Mathematica
    Flatten[Table[Range[Ceiling[Sqrt[7 10^n]],Floor[Sqrt[8 10^n]]]^2,{n,5}]] (* Harvey P. Dale, Jun 15 2011 *)

Formula

a(n) = A045861(n)^2. - Michel Marcus, Sep 04 2021

A045792 Squares with initial digit '8'.

Original entry on oeis.org

81, 841, 8100, 8281, 8464, 8649, 8836, 80089, 80656, 81225, 81796, 82369, 82944, 83521, 84100, 84681, 85264, 85849, 86436, 87025, 87616, 88209, 88804, 89401, 801025, 802816, 804609, 806404, 808201, 810000, 811801, 813604, 815409, 817216
Offset: 1

Views

Author

Jeff Burch

Keywords

Crossrefs

Cf. A045862.
Cf. A045784, A045785, A045786, A045787, A045788, A045789, A045791, A045793.

Formula

a(n) = A045862(n)^2. - Michel Marcus, Sep 04 2021

Extensions

a(16) corrected by Sean A. Irvine, Mar 21 2021
Offset 1 from Michel Marcus, Mar 22 2021

A045863 Numbers whose square has initial digit '9'.

Original entry on oeis.org

3, 30, 31, 95, 96, 97, 98, 99, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976
Offset: 1

Views

Author

Jeff Burch

Keywords

Links

Crossrefs

Cf. A045793.

Programs

  • Mathematica
    id9[n_]:=Module[{min=Floor[Sqrt[9*10^n]],max=Floor[Sqrt[10*10^n]]}, Select[ Range[ min,max], First[IntegerDigits[#^2]]==9&]]; Flatten[ Table[ id9[n],{n,0,5}]] (* Harvey P. Dale, May 29 2013 *)
  • PARI
    list(lim)=my(v=List()); for(d=1,2*#digits(lim\=1), for(n=sqrtint(9*10^(d-1)-1)+1, min(sqrtint(10^d-1), lim), listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Nov 03 2021

A333663 a(1) = 1, then a(n) is the smallest square not occurring earlier and starting with the last nonzero digit of a(n-1).

Original entry on oeis.org

1, 16, 64, 4, 49, 9, 900, 961, 100, 121, 144, 400, 441, 169, 9025, 529, 9216, 625, 576, 676, 6084, 484, 4096, 6241, 196, 6400, 4225, 5041, 1024, 4356, 6561, 1089, 9409, 9604, 4489, 9801, 1156, 6724, 4624, 4761, 1225, 5184, 4900, 90000, 90601, 1296, 6889, 91204
Offset: 1

Views

Author

Bernard Schott, Sep 03 2020

Keywords

Comments

Every term begins with 1, 4, 5, 6 or 9.

Examples

			The smallest square not yet in the data that begins with 1 is 16, hence a(2) = 16.

Links

Crossrefs

Cf. A155985 (variant).
Subsequences of squares with initial digit k: A045784 (k=1), A045787 (k=4), A045788 (k=5), A045789 (k=6), A045793 (k=9).

Programs

  • Mathematica
    Nest[Block[{a = #, k = 1, d = Mod[#[[-1]]/10^IntegerExponent[#[[-1]] ], 10]}, While[Nand[FreeQ[a, #], d == Floor[#/10^(IntegerLength[#] - 1)] ] &[k^2], k++]; Append[a, k^2]] &, {1}, 47] (* Michael De Vlieger, Sep 11 2020 *)
  • PARI
    nxt(va, d) = {my(k=1); while ((digits(k^2)[1]!=d) || #select(x->(x==k^2), va), k++); k^2;}
lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = nxt(va, digits(fromdigits(Vecrev(digits(va[n-1]))))[1]);); va;} \\ Michel Marcus, Sep 04 2020

Extensions

More terms from Michel Marcus, Sep 04 2020
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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