A343740 a(n) is the digit position of the first appearance of the last digit to appear in sqrt(n) (or -1 if n is a square).
-1, 19, 23, -1, 37, 39, 45, 36, -1, 27, 17, 25, 15, 36, 19, -1, 20, 36, 25, 37, 28, 13, 27, 52, -1, 39, 17, 38, 27, 26, 17, 23, 24, 37, 19, -1, 25, 26, 26, 41, 58, 57, 25, 12, 25, 22, 24, 19, -1, 33, 48, 23, 41, 49, 23, 32, 32, 23, 30, 19, 17, 31, 27, -1, 24
Offset: 1
Examples
a(2)=19 because A343739(2)=8 and the first appearance of an 8 in sqrt(2) = 1.414213562373095048... is at the 19th digit; a(24)=52 because A343739(24)=0 and the first appearance of a 0 in sqrt(24) = 4.898979485566356196394568149411782783931894961313340... is at the 52nd digit.
Programs
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Mathematica
Table[If[IntegerQ@ Sqrt@ n, -1, Function[s, Max@ Array[FirstPosition[s, #][[1]] &, 10, 0]]@ RealDigits[Sqrt[n], 10, 120][[1]]], {n, 65}] (* Michael De Vlieger, Jul 06 2021 *)
Formula
a(100^q*n) = a(n), q > 0. - Bernard Schott, Jul 29 2021
Comments