A122115 -id:A122115 - cp's OEIS frontend

A293506 Decimal expansion of real root of x^5 - x^4 - x^2 - 1.

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

Offset: 1

Iain Fox, Oct 10 2017

This root is also the ninth smallest of the Pisot numbers.

The ratio of successive terms of A122115 converges to this number.

			1.570147312196054362910665...

Iain Fox, Table of n, a(n) for n = 1..20000
Hans Walser, Funktionenfolge [in German]
Eric Weisstein's World of Mathematics, Pisot Number.
Wikipedia, Pisot-Vijayaraghavan number
Index entries for algebraic numbers, degree 5

Cf. A060006, A086106, A228777, A092526, A293508, A293509, A293557, A122115, A293560 (inverse).

First@ RealDigits[Root[#^5 - #^4 - #^2 - 1 &, 1], 10, 87] (* Michael De Vlieger, Oct 23 2017 *)

solve(x=1, 2, x^5 - x^4 - x^2 - 1) \\ Michel Marcus, Oct 11 2017

default(realprecision, 20080); x=solve(x=1, 2, x^5 - x^4 - x^2 - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b293506.txt", n, " ", d));

More terms from Andrey Zabolotskiy, Oct 12 2017

A104101 The Lost Numbers.

Original entry on oeis.org

4, 8, 15, 16, 23, 42

Offset: 0

Marcus Dicander, Mar 04 2005

These numbers were central to the plot of the TV-series "Lost", episodes 18 and 201.
Another number in the sequence, perhaps the next one, is 540: the number of days which the team of two people who are addressed by the orientation film are to stay at station 3. 4+8+15+16+23+42 = 108 and 108 * 5 = 540. - Joshua Walton (joshuawalton(AT)hotmail.com), May 05 2006
According to the show, 108 is not officially a part of the sequence, it just happens to be the sum of those numbers. - Ville Saalo (vsaalo(AT)iki.fi), Nov 19 2006
For n = 0,1,2,3,4,5 (1/120)(42n^5 - 305n^4 + 1100n^3 - 895n^2 + 1018n + 480) gives 4,12,35,89,213,511 -- the binomial transform of 4,8,15,16,23,42. The sequence continues 1194,2622,5346,10150,18093.... The polynomial (1/120)(42x^5 - 305x^4 + 1100x^3 - 895x^2 + 1018x + 480) is the "Shaw-Basho polynomial". - Ross La Haye, Feb 26 2007

Marcus Dicander, The Lost Numbers: 4 8 15 16 23 42
Lostpedia contributors, "The Numbers", Lostpedia
Doug Shaw, The Lost Sequence
Wikipedia, Mythology of Lost

Cf. A122115, A130826.

It is easy to fit formulas to the first six terms, in a million different ways, but none of them are of any interest (the seventh term can be chosen to be any number you wish). - N. J. A. Sloane, Oct 22 2017

cp's OEIS Frontend

A293506 Decimal expansion of real root of x^5 - x^4 - x^2 - 1.

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