A034096 Fractional part of square root of n starts with digit 0 (squares excluded).

26, 37, 50, 65, 82, 101, 102, 122, 123, 145, 146, 170, 171, 197, 198, 226, 227, 228, 257, 258, 259, 290, 291, 292, 325, 326, 327, 362, 363, 364, 401, 402, 403, 404, 442, 443, 444, 445, 485, 486, 487, 488, 530, 531, 532, 533, 577, 578, 579, 580, 626, 627

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• easy
• base

Comments

Given n > 4, n^2 + 1 is in the sequence. In fact, as n gets larger, more and more numbers just above n^2 are also in the sequence. For a particular n, the integers between n^2 and (n + 1/10)^2 are in this sequence. - Alonso del Arte, Mar 16 2019

Examples

			sqrt(145) = 12.041594578792295..., so 145 is in the sequence.
sqrt(146) = 12.083045973594572..., so 146 is also in the sequence.
sqrt(147) = 12.124355652982141..., so 147 is not in the sequence.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023961, A034106.

Programs

Maple

A034096 := proc(n) option remember: local k,rt: if(n=1)then return 26: else k:=procname(n-1)+1: do rt:=sqrt(k): if(not frac(rt)=0 and floor(10*rt) mod 10 = 0)then return k: fi: k:=k+1: od: fi: end: seq(A034096(n), n=1..50); # Nathaniel Johnston, May 04 2011
seq(seq(x, x=floor(n^2) +1 .. ceil((n+1/10)^2)-1),n=1..100); # Robert Israel, Sep 21 2015

Mathematica

zdQ[n_] := Module[{c = Sqrt[n], sr, i, l}, sr = RealDigits[c, 10, 5]; i = Last[sr] + 1; l = First[sr]; l[[i]] == 0 && !IntegerQ[c]]; Select[Range[700], zdQ] (* Harvey P. Dale, Oct 10 2011 *)
Flatten[Table[Range[n^2 + 1, Floor[(n + 1/10)^2]], {n, 25}]] (* Alonso del Arte, Mar 16 2019 *)

PARI

isok(n) = !issquare(n) && !(floor(10*sqrt(n)) % 10); \\ Michel Marcus, Sep 21 2015

PARI

is(n)=my(s=sqrtint(n),s2=s^2); s2+s\5 >= n && s2 < n \\ Charles R Greathouse IV, Sep 07 2022

PARI

list(lim)=my(v=List(),s=sqrtint(lim\=1)); for(n=5,s-1, for(i=n^2+1,n^2+n\5, listput(v,i))); for(i=s^2+1,min(s^2+s\5,lim), listput(v,i)); Vec(v) \\ Charles R Greathouse IV, Sep 08 2022

Formula

A023961(a(n)) = 0. - Michel Marcus, Sep 21 2015

a(n) = 10n + O(sqrt(n)). - Charles R Greathouse IV, Sep 08 2022

Extensions

Name clarified by Michel Marcus, Sep 21 2015