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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 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 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 March 29 12:12 EDT 2023. Contains 361599 sequences. (Running on oeis4.)