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%I #36 Sep 08 2022 16:49:43
%S 26,37,50,65,82,101,102,122,123,145,146,170,171,197,198,226,227,228,
%T 257,258,259,290,291,292,325,326,327,362,363,364,401,402,403,404,442,
%U 443,444,445,485,486,487,488,530,531,532,533,577,578,579,580,626,627
%N Fractional part of square root of n starts with digit 0 (squares excluded).
%C 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
%H Nathaniel Johnston, <a href="/A034096/b034096.txt">Table of n, a(n) for n = 1..10000</a>
%F A023961(a(n)) = 0. - _Michel Marcus_, Sep 21 2015
%F a(n) = 10n + O(sqrt(n)). - _Charles R Greathouse IV_, Sep 08 2022
%e sqrt(145) = 12.041594578792295..., so 145 is in the sequence.
%e sqrt(146) = 12.083045973594572..., so 146 is also in the sequence.
%e sqrt(147) = 12.124355652982141..., so 147 is not in the sequence.
%p 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
%p seq(seq(x, x=floor(n^2) +1 .. ceil((n+1/10)^2)-1),n=1..100); # _Robert Israel_, Sep 21 2015
%t 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 *)
%t Flatten[Table[Range[n^2 + 1, Floor[(n + 1/10)^2]], {n, 25}]] (* _Alonso del Arte_, Mar 16 2019 *)
%o (PARI) isok(n) = !issquare(n) && !(floor(10*sqrt(n)) % 10); \\ _Michel Marcus_, Sep 21 2015
%o (PARI) is(n)=my(s=sqrtint(n),s2=s^2); s2+s\5 >= n && s2 < n \\ _Charles R Greathouse IV_, Sep 07 2022
%o (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
%Y Cf. A023961, A034106.
%K nonn,easy,base
%O 1,1
%A _Patrick De Geest_, Sep 15 1998
%E Name clarified by _Michel Marcus_, Sep 21 2015
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