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A034096
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Fractional part of square root of n starts with digit 0 (squares excluded).
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13
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 1..10000
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FORMULA
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A023961(a(n)) = 0. - Michel Marcus, Sep 21 2015
a(n) = 10n + O(sqrt(n)). - Charles R Greathouse IV, Sep 08 2022
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A023961, A034106.
Sequence in context: A046468 A138065 A240897 * A034106 A239604 A213012
Adjacent sequences: A034093 A034094 A034095 * A034097 A034098 A034099
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KEYWORD
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nonn,easy,base
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AUTHOR
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Patrick De Geest, Sep 15 1998
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EXTENSIONS
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Name clarified by Michel Marcus, Sep 21 2015
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STATUS
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approved
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