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

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

1,1

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

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Patrick De Geest, Numbers whose digits occur with same frequency

Example

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

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 *)

Crossrefs

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

Sequence in context: A116065 A234777 A234770 * A046378 A187176 A236009

Adjacent sequences: A052046 A052047 A052048 * A052050 A052051 A052052

Keyword

nonn,base,fini

Author

Patrick De Geest, Dec 15 1999

Status

approved