A111896 -id:A111896 - cp's OEIS frontend

A111862 Second digit after decimal point of square root of n in decimal representation.

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

Offset: 1

Reinhard Zumkeller, Aug 20 2005

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

Cf. A023961, A111890, A111891, A111892, A111893, A111894, A111895, A111896, A111897, A111898, A111899.

A111862 := proc(n) return floor(100*sqrt(n)) mod 10: end: seq(A111862(n), n=1..100); # Nathaniel Johnston, May 04 2011

Mod[Floor[100*Sqrt[Range[100]]], 10] (* Paolo Xausa, May 17 2024 *)

A111856 Number of numbers m <= n such that 6 equals the first digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 11, 11, 11

Offset: 1

Reinhard Zumkeller, Aug 20 2005

			a(10) = 1, a(100) = 11, a(1000) = 101, a(10000) = 1010.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A111850, A111851, A111852, A111853, A111854, A111855, A111857, A111858, A111859, A111896.

Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 6] &, 100]] (* Paolo Xausa, May 17 2024 *)

For n > 1: if A023961(n)=6 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Limit_{n->oo} a(n)/n = 1/10.

A111892 Number of numbers m <= n such that 2 equals the second digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Reinhard Zumkeller, Aug 20 2005

For n > 1: if A111862(n)=2 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Lim_{n->infinity} a(n)/n = 1/10.

			a(10) = 1, a(100) = 7, a(1000) = 95, a(10000) = 1000.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A111862, A111890, A111891, A111893, A111894, A111895, A111896, A111897, A111898, A111899, A111852.

Accumulate[Table[If[NumberDigit[Sqrt[n],-2]==2,1,0],{n,110}]] (* Harvey P. Dale, Nov 22 2021 *)

A111899 Number of numbers m <= n such that 9 equals the second digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11

Offset: 1

Reinhard Zumkeller, Aug 20 2005

			a(10) = 0, a(100) = 10, a(1000) = 106, a(10000) = 994.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111895, A111896, A111897, A111898, A111859.

Accumulate[Array[Boole[Mod[Floor[100*Sqrt[#]], 10] == 9] &, 100]] (* Paolo Xausa, May 17 2024 *)

For n > 1: if A111862(n) = 9 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Limit_{n->oo} a(n)/n = 1/10.

A111890 Number of numbers m <= n such that 0 equals the second digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14

Offset: 1

Reinhard Zumkeller, Aug 20 2005

For n > 1: if A111862(n)=4 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Lim_{n->infinity} a(n)/n = 1/10.

			a(10) = 3, a(100) = 15, a(1000) = 104, a(10000) = 1006.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Cf. A111891, A111892, A111893, A111894, A111895, A111896, A111897, A111898, A111899, A111850.

A111891 Number of numbers m <= n such that 1 equals the second digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset: 1

Reinhard Zumkeller, Aug 20 2005

For n > 1: if A111862(n)=1 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Lim_{n->infinity} a(n)/n = 1/10.

			a(10) = 1, a(100) = 10, a(1000) = 100, a(10000) = 998.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Cf. A111862, A111890, A111892, A111893, A111894, A111895, A111896, A111897, A111898, A111899, A111851.

Accumulate[Table[If[NumberDigit[Sqrt[n],-2]==1,1,0],{n,100}]] (* Harvey P. Dale, Mar 31 2022 *)

A111893 Number of numbers m <= n such that 3 equals the second digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, Aug 20 2005

For n > 1: if A111862(n)=3 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Lim_{n->infinity} a(n)/n = 1/10.

			a(10) = 2, a(100) = 8, a(1000) = 103, a(10000) = 1000.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Cf. A111862, A111890, A111891, A111892, A111894, A111895, A111896, A111897, A111898, A111899, A111853.

Accumulate[Table[If[Mod[Floor[100N[Sqrt[n],10]],10]==3,1,0],{n,120}]] (* Harvey P. Dale, Mar 04 2015 *)

A111894 Number of numbers m <= n such that 4 equals the second digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13

Offset: 1

Reinhard Zumkeller, Aug 20 2005

			a(10) = 2, a(100) = 17, a(1000) = 121, a(10000) = 1066.

Cf. A111890, A111891, A111892, A111893, A111895, A111896, A111897, A111898, A111899, A111854.

A111895 Number of numbers m <= n such that 5 equals the second digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Reinhard Zumkeller, Aug 20 2005

For n > 1: if A111862(n)=5 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Lim_{n->infinity} a(n)/n = 1/10.

			a(10) = 0, a(100) = 5, a(1000) = 79, a(10000) = 934.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111896, A111897, A111898, A111899, A111855.

A111897 Number of numbers m <= n such that 7 equals the second digit after decimal point of square root of n in decimal representation.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Reinhard Zumkeller, Aug 20 2005

For n > 1: if A111862(n)=7 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Lim_{n->infinity} a(n)/n = 1/10.

			a(10) = 0, a(100) = 7, a(1000) = 100, a(10000) = 1000.

G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111895, A111896, A111898, A111899, A111857.

Accumulate[Table[If[Mod[IntegerPart[100*Sqrt[n]],10]==7,1,0],{n,110}]] (* Harvey P. Dale, Oct 16 2014 *)

cp's OEIS Frontend

A111862 Second digit after decimal point of square root of n in decimal representation.

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A111856 Number of numbers m <= n such that 6 equals the first digit after decimal point of square root of n in decimal representation.

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A111892 Number of numbers m <= n such that 2 equals the second digit after decimal point of square root of n in decimal representation.

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A111899 Number of numbers m <= n such that 9 equals the second digit after decimal point of square root of n in decimal representation.

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A111890 Number of numbers m <= n such that 0 equals the second digit after decimal point of square root of n in decimal representation.

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A111891 Number of numbers m <= n such that 1 equals the second digit after decimal point of square root of n in decimal representation.

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A111893 Number of numbers m <= n such that 3 equals the second digit after decimal point of square root of n in decimal representation.

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A111894 Number of numbers m <= n such that 4 equals the second digit after decimal point of square root of n in decimal representation.

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A111895 Number of numbers m <= n such that 5 equals the second digit after decimal point of square root of n in decimal representation.

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