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A034096 Fractional part of square root of n starts with digit 0 (squares excluded). 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

PROG

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

CROSSREFS

Cf. A023961, A034106.

Sequence in context: A046468 A138065 A240897 * A034106 A239604 A213012

Adjacent sequences:  A034093 A034094 A034095 * A034097 A034098 A034099

KEYWORD

nonn,easy,base

AUTHOR

Patrick De Geest, Sep 15 1998

EXTENSIONS

Name clarified by Michel Marcus, Sep 21 2015

STATUS

approved

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Last modified January 18 17:18 EST 2022. Contains 350455 sequences. (Running on oeis4.)