A343742 -id:A343742 - cp's OEIS frontend

A343739 a(n) is the last digit to appear in sqrt(n) (or -1 if n is a square).

-1, 8, 4, -1, 5, 6, 8, 5, -1, 4, 8, 2, 8, 0, 5, -1, 8, 3, 1, 0, 3, 3, 6, 0, -1, 6, 8, 4, 9, 8, 9, 7, 1, 6, 2, -1, 4, 3, 1, 1, 9, 1, 9, 1, 1, 4, 7, 4, -1, 9, 0, 4, 6, 0, 3, 0, 1, 4, 3, 0, 3, 2, 6, -1, 1, 7, 0, 7, 5, 1, 0, 6, 9, 9, 9, 5, 5, 9, 2, 3, -1, 2, 6, 2

Offset: 1

Jon E. Schoenfield, Jul 05 2021

For the digit position in sqrt(n) at which the digit a(n) first appears, see A343740.

			a(2)=8 because 8 is the last digit to appear in sqrt(2) = 1.414213562373095048...;
a(24)=0 because 0 is the last digit to appear in sqrt(24) = 4.898979485566356196394568149411782783931894961313340...

Cf. A023961, A343740, A343741, A343742.

Table[If[IntegerQ@ Sqrt@ n, -1, Function[s, FirstPosition[#, Max@ #][[1]] - 1 &@ Array[FirstPosition[s, #][[1]] &, 10, 0]]@ RealDigits[Sqrt[n], 10, 120][[1]]], {n, 84}] (* Michael De Vlieger, Jul 06 2021 *)

a(100^q*n) = a(n), q > 0. - Bernard Schott, Jul 24 2021

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).

Original entry on oeis.org

-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

Jon E. Schoenfield, Jul 05 2021

A343739(n) is the last digit to appear in the decimal expansion of sqrt(n) (or -1 if n is a square), so a(n) is the digit position of the first appearance of the digit A343739(n) in sqrt(n).

(The first digit of sqrt(n) is counted as digit position 1; the decimal point is disregarded.)

			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.

Cf. A023961, A343739, A343741, A343742.

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 *)

a(100^q*n) = a(n), q > 0. - Bernard Schott, Jul 29 2021

A343741 Record high values in A343740.

Original entry on oeis.org

19, 23, 37, 39, 45, 52, 58, 69, 110, 118, 132, 133, 136, 139, 143, 152, 158, 164, 169, 173, 174, 187, 195, 204, 215, 217

Offset: 1

Jon E. Schoenfield, Jul 05 2021

Cf. A343739, A343740, A343742.

Rest@ Union@ FoldList[Max, Table[If[IntegerQ@ Sqrt@ n, -1, Function[s, Max@ Array[FirstPosition[s, #][[1]] &, 10, 0]]@ RealDigits[Sqrt[n], 10, 300][[1]]], {n, 10^5}]] (* Michael De Vlieger, Jul 06 2021 *)

a(24)-a(26) from Chai Wah Wu, Jul 06 2021

cp's OEIS Frontend

A343739 a(n) is the last digit to appear in sqrt(n) (or -1 if n is a square).

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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).

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Programs

Mathematica

Formula

A343741 Record high values in A343740.

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