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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
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
FORMULA
A023961(a(n)) = 0. - Michel Marcus, Sep 21 2015
a(n) = 10n + O(sqrt(n)). - Charles R Greathouse IV, Sep 08 2022
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
(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
CROSSREFS
Sequence in context: A046468 A138065 A240897 * A034106 A239604 A213012
KEYWORD
nonn,easy,base
AUTHOR
Patrick De Geest, Sep 15 1998
EXTENSIONS
Name clarified by Michel Marcus, Sep 21 2015
STATUS
approved