A034101 Numbers whose fractional part of square root starts with digit 5.

21, 31, 43, 57, 73, 91, 92, 111, 112, 133, 134, 157, 158, 183, 184, 211, 212, 213, 241, 242, 243, 273, 274, 275, 307, 308, 309, 343, 344, 345, 381, 382, 383, 384, 421, 422, 423, 424, 463, 464, 465, 466, 507, 508, 509, 510, 553, 554, 555, 556, 601, 602, 603

Offset

1,1

Comments

The sequence has increasingly long runs of consecutive integers, followed by a roughly 10 times larger jump. Therefore the graph looks like a (roughly self-similar) staircase with increasingly larger steps, which however become smaller (closer to a straight line) upon "zooming out". - M. F. Hasler, Sep 04 2025

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1001 [offset to 1 adapted by Georg Fischer, Sep 03 2020]

Formula

a(n) ~ 10*n. - M. F. Hasler, Sep 04 2025

Mathematica

fp5Q[n_]:=Module[{rd=RealDigits[N[FractionalPart[Sqrt[n]]]]}, rd[[2]]==0 && First[rd[[1]]]==5]; Select[Range[700], fp5Q] (* Harvey P. Dale, Jan 11 2013 *)

Prog

(PARI) A034101_first(N)=vector(N, i, if(i>1, while(sqrtint(100*N++)%10!=5, ); N, N=21)) \\ M. F. Hasler, Sep 04 2025

Crossrefs

Cf. A034111 (first term of runs).

Sequence in context: A336383 A168000 A031889 * A034111 A077687 A113762

Adjacent sequences: A034098 A034099 A034100 * A034102 A034103 A034104

Keyword

nonn,easy,base

Author

Patrick De Geest, Sep 15 1998

Status

approved