A209927 -id:A209927 - cp's OEIS frontend

A209926 Concatenation of the months' names, spelled in French, with 'a'=1, ..., 'z'=26 (ignoring accents).

10, 1, 14, 22, 9, 5, 18, 6, 5, 22, 18, 9, 5, 18, 13, 1, 18, 19, 1, 22, 18, 9, 12, 13, 1, 9, 10, 21, 9, 14, 10, 21, 9, 12, 12, 5, 20, 1, 15, 21, 20, 19, 5, 16, 20, 5, 13, 2, 18, 5, 15, 3, 20, 15, 2, 18, 5, 14, 15, 22, 5, 13, 2, 18, 5, 4, 5, 3, 5, 13, 2, 18, 5

Offset: 1

M. F. Hasler, Mar 15 2012

Cf. A209924 (same for English), A209927 (same for German).

Cf. A031139, A049004, A033986, A089746, A049005, A069195, A103742, A134456, A161376.

Vec( Vecsmall( "janvierfevriermarsavrilmaijuinjuilletaoutseptembreoctobrenovembredecembre" ))%32

A365750 Decimal expansion of the largest root of the polynomial x^3 - x^2 - 3*x + 1.

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Sep 19 2023

It is the spectral radius of the paw graph.

			2.1700864866260337227032557644253...

Alberto Seeger and David Sossa, Infinite families of connected graphs with equal spectral radius, Australas. J. Combin. 87 (2) (2023), 258-276. See p. 260.
Eric Weisstein's World of Mathematics, Paw Graph

Cf. A010467, A209927, A222132, A352667, A365814.

First[RealDigits[1/3+2/3Sqrt[10]Cos[1/3ArcCos[10^(-3/2)]],10,88]]

Equals 1/3 + (2/3)*sqrt(10)*cos((1/3)*arccos(10^(-3/2))).

A365814 Decimal expansion of the largest root of the polynomial x^3 - 2x^2 - 2x + 2.

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Sep 19 2023

It is the spectral radius of the house graph.

			2.4811943040920156226335372412168571805527452...

Alberto Seeger and David Sossa, Infinite families of connected graphs with equal spectral radius, Australas. J. Combin. 87 (2) (2023), 258-276. See p. 270.
Eric Weisstein's World of Mathematics, House Graph

Cf. A078564, A209927, A222132, A365750.

Digits:= 140:
fsolve(x^3-2*x^2-2*x+2)[3];  # Alois P. Heinz, Sep 19 2023

First[RealDigits[Root[#^3-2#^2-2#+2,3,0],10,88]]

Equals (2 + 10/(3*i*sqrt(111) - 1)^(1/3) + (3*i*sqrt(111) - 1)^(1/3))/3, where i denotes the imaginary unit.

A320029 Decimal expansion of sqrt(9 + sqrt(9 + sqrt(9 + sqrt(9 + ...)))) = (sqrt(37) + 1)/2.

Original entry on oeis.org

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

Offset: 1

Robert G. Wilson v, Oct 03 2018

For x >= 0, sqrt(x + sqrt(x + sqrt(x + sqrt(x + ...)))) = (sqrt(4*x+1) + 1)/2. This is an integer for each x such that 2*x is a term in A000217.

			3.541381265149109844499842122601033531042485047393205593209576523243166362659...

Index entries for algebraic numbers, degree 2

Cf. A000007, A001622, A000038, A209927, A222132, A222134, A223140, A235162.

evalf((sqrt(37)+1)/2,120); # Muniru A Asiru, Oct 07 2018

RealDigits[ Fold[ Sqrt[#1 + #2] &, 0, Table[9, {135}]], 10, 111][[1]] (* or *)
RealDigits[(Sqrt[37] + 1)/2, 10, 111][[1]]

(sqrt(37)+1)/2 \\ Altug Alkan, Oct 03 2018

Minimal polynomial: x^2 - x - 9. - Stefano Spezia, Jul 02 2025

cp's OEIS Frontend

A209926 Concatenation of the months' names, spelled in French, with 'a'=1, ..., 'z'=26 (ignoring accents).

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A365750 Decimal expansion of the largest root of the polynomial x^3 - x^2 - 3*x + 1.

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A365814 Decimal expansion of the largest root of the polynomial x^3 - 2*x^2 - 2*x + 2.

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A320029 Decimal expansion of sqrt(9 + sqrt(9 + sqrt(9 + sqrt(9 + ...)))) = (sqrt(37) + 1)/2.

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Maple

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PARI

Formula

A365814 Decimal expansion of the largest root of the polynomial x^3 - 2x^2 - 2x + 2.