A023961 - OEIS

%I #35 Oct 28 2019 11:27:04

%S 0,4,7,0,2,4,6,8,0,1,3,4,6,7,8,0,1,2,3,4,5,6,7,8,0,0,1,2,3,4,5,6,7,8,

%T 9,0,0,1,2,3,4,4,5,6,7,7,8,9,0,0,1,2,2,3,4,4,5,6,6,7,8,8,9,0,0,1,1,2,

%U 3,3,4,4,5,6,6,7,7,8,8,9,0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,0,0,0,1,1,2

%N First digit after decimal point of square root of n.

%C When n is a square, a(n) is equal to 0, but the converse is not true, see A034096. - _Michel Marcus_, Sep 21 2015

%H Nathaniel Johnston, <a href="/A023961/b023961.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A010879(A000196(100*n)). - _Robert Israel_, Jul 30 2015

%e sqrt(1) = 1.00000000... hence a(1) = 0.

%e sqrt(2) = 1.41421356... hence a(2) = 4.

%e sqrt(3) = 1.73205080... hence a(3) = 7.

%e sqrt(4) = 2.00000000... hence a(4) = 0.

%e Note that 26 = 2 * 13 and sqrt(26) = 5.09901951... so a(26) = 0 even though 26 is not a perfect square.

%p A023961 := proc(n) return floor(10*sqrt(n)) mod 10: end: seq(A023961(n),n=1..100); # _Nathaniel Johnston_, May 04 2011

%t Array[Function[n, RealDigits[N[Power[n, 1/2], 10], 10] // (#[[1, #[[2]] + 1]]) &], 110]

%t fd[n_] := Module[{rd = RealDigits[Sqrt[n], 10, 10]}, First[rd][[Last[rd] + 1]]]; Array[fd, 90] (* _Harvey P. Dale_, Jan 16 2014 *)

%o (PARI) a(n) = floor(10*sqrt(n)) % 10; \\ _Michel Marcus_, Sep 21 2015

%Y Cf. A111862, A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111859.

%K nonn,easy,base

%O 1,2

%A _N. J. A. Sloane_, _Olivier Gérard_