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 1-5 of 5 results.

A052049 a(n)^2 is a square whose digits occur with an equal minimum frequency of 2.

Original entry on oeis.org

88, 478, 577, 583, 715, 836, 880, 881, 893, 3362, 3386, 3911, 4077, 4780, 5077, 5239, 5369, 5770, 5784, 5789, 5830, 5858, 6523, 6756, 6772, 6926, 6941, 7107, 7150, 7359, 7535, 7827, 8043, 8196, 8229, 8360, 8525, 8810, 8930, 8989, 9251, 9701, 9764, 9786
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1999

Keywords

Comments

There are A225428(10) = 597959 terms in this sequence. The last term is 9994363488, whose square is 99887301530267526144 = A052050(597959). - Hugo Pfoertner, May 12 2023

Examples

			577^2 = 332929, which contains each of its digits (2, 3, and 9) twice, so 577 is in this sequence.

Links

Crossrefs

Cf. A045540, A052046, A052047, A052048, A052050, A052051, A052052, A225428.

Programs

  • Maple
    isA052049 := proc(n) local d, k, fr, eqfr: d:=convert(n^2, base, 10): eqfr:=true: fr:=numboccur(d[1], d): if(fr=1)then return false: fi: for k from 0 to 9 do if(not member(numboccur(k, d), {fr, 0}))then eqfr:=false: break: fi: od: return eqfr: end: seq(`if`(isA052049(n), n, NULL), n=1..9800); # Nathaniel Johnston, Jun 02 2011
  • Mathematica
    ta[n_]:=DeleteDuplicates[Transpose[Tally[IntegerDigits[n^2]]][[2]]]; t ={}; Do[If[Length[x=ta[n]]==1 && x[[1]]>=2, AppendTo[t,n]],{n,9800}]; t (* Jayanta Basu, May 11 2013 *)

A052050 Squares whose digits occur with an equal minimal frequency of 2.

Original entry on oeis.org

7744, 228484, 332929, 339889, 511225, 698896, 774400, 776161, 797449, 11303044, 11464996, 15295921, 16621929, 22848400, 25775929, 27447121, 28826161, 33292900, 33454656, 33512521, 33988900, 34316164, 42549529, 45643536, 45859984, 47969476, 48177481, 50509449, 51122500
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1999

Keywords

Comments

There are A225428(10)=597959 terms in this sequence. The last term is 99887301530267526144 = 9994363488^2. - Hugo Pfoertner, May 12 2023

Links

Crossrefs

Cf. A052049, A045540, A052046, A052047, A052048, A052051, A052052, A225428.

Programs

  • Mathematica
    Select[Table[n^2, {n, 6760}], Union[Last[Transpose[Tally[IntegerDigits[#]]]]] == {2} &] (* Jayanta Basu, Jun 17 2013 *)
  • Python
    from itertools import islice
from collections import Counter
def afull(): yield from (x**2 for x in range(10**10) if set(Counter(str(x**2)).values()) == {2})
print(list(islice(afull(), 47))) # Michael S. Branicky, May 12 2023

A226796 Number of nonnegative numbers x < 10^n such that the digits of x^2 occur with an equal frequency of 1.

Original entry on oeis.org

10, 59, 221, 441, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611, 611
Offset: 1

Views

Author

T. D. Noe, Jun 21 2013

Keywords

Examples

			All numbers 0 to 9 have squares containing only digits of frequency 1: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81. See A119509 for the positive terms.

Crossrefs

Cf. A119509 (positive terms x), A225428 (for 2 digits).

Programs

  • Mathematica
    cnt = 0; x = 0; Table[While[x < 10^n, If[Union[Last[Transpose[Tally[IntegerDigits[x^2]]]]] == {1}, cnt++]; x++]; cnt, {n, 5}]

A225429 Number of n-digit numbers x such that the digits of x^2 occur with frequency 2.

Original entry on oeis.org

0, 1, 8, 38, 165, 1020, 5360, 24553, 98442
Offset: 1

Views

Author

T. D. Noe, Jun 21 2013

Keywords

Comments

After a(10), all terms are 0.

Examples

			The only two-digit number is 88, whose square is 7744.

Crossrefs

Cf. A225428.

Programs

  • Mathematica
    cnt = 0; t2 = Table[x = Floor[Sqrt[10] * 10^(n-1)]; While[x < 10^n, If[Union[Last[Transpose[Tally[IntegerDigits[x^2]]]]] == {2}, cnt++]; x++]; cnt, {n, 6}]; Join[{0}, Differences[t2]]

A226797 Number of n-digit numbers x such that the digits of x^2 occur with frequency 1.

Original entry on oeis.org

10, 49, 162, 220, 170, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

T. D. Noe, Jun 21 2013

Keywords

Comments

After a(5), all terms are 0.

Examples

			All numbers 0 to 9 have squares containing only digits of frequency 1: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81.

Crossrefs

Cf. A225428, A226796.

Programs

  • Mathematica
    cnt = 0; x = 0; t2 = Table[While[x < 10^n, If[Union[Last[Transpose[Tally[IntegerDigits[x^2]]]]] == {1}, cnt++]; x++]; cnt, {n, 5}]; Differences[Join[{0}, t2]]
Showing 1-5 of 5 results.

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

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