A023961 First digit after decimal point of square root of n.

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, 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, 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

Offset

1,2

Comments

When n is a square, a(n) is equal to 0, but the converse is not true, see A034096. - Michel Marcus, Sep 21 2015

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Formula

a(n) = A010879(A000196(100*n)). - Robert Israel, Jul 30 2015

Example

sqrt(1) = 1.00000000... hence a(1) = 0.
sqrt(2) = 1.41421356... hence a(2) = 4.
sqrt(3) = 1.73205080... hence a(3) = 7.
sqrt(4) = 2.00000000... hence a(4) = 0.
Note that 26 = 2 * 13 and sqrt(26) = 5.09901951... so a(26) = 0 even though 26 is not a perfect square.

Maple

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

Mathematica

Array[Function[n, RealDigits[N[Power[n, 1/2], 10], 10] // (#[[1, #[[2]] + 1]]) &], 110]
fd[n_] := Module[{rd = RealDigits[Sqrt[n], 10, 10]}, First[rd][[Last[rd] + 1]]]; Array[fd, 90] (* Harvey P. Dale, Jan 16 2014 *)

Prog

(PARI) a(n) = floor(10*sqrt(n)) % 10; \\ Michel Marcus, Sep 21 2015

Crossrefs

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

Sequence in context: A069179 A336764 A058377 * A147863 A358662 A019976

Adjacent sequences: A023958 A023959 A023960 * A023962 A023963 A023964

Keyword

nonn,easy,base

Author

N. J. A. Sloane, Olivier Gérard

Status

approved