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

Author

Patrick De Geest, Dec 15 1999

Keywords

• nonn
• base
• fini

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

• Nathaniel Johnston, Table of n, a(n) for n = 1..5000
• Patrick De Geest, Numbers whose digits occur with same frequency

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 *)