A346442 -id:A346442

Search: a346442 -id:a346442

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A346443

Decimal expansion of the function value corresponding to A346442, negated.

+20
4

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

-1,2

COMMENTS

See A346442 for more information and references.

LINKS

Table of n, a(n) for n=-1..93.

EXAMPLE

-0.015866920833695758383163574261086263572492773777798912858...

CROSSREFS

Cf. A346442, A346444, A346445, A346663.

KEYWORD

nonn,cons

AUTHOR

Hugo Pfoertner, Jul 18 2021

STATUS

approved

A346444

Decimal expansion, negated, of the smaller real root of the polynomial of A346442.

+20
4

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

See A346442 for more information and references.

LINKS

Table of n, a(n) for n=0..87.

EXAMPLE

-0.99669126804203510224363267899071774051686056837859678314752...

PROG

(PARI) P(n, x) = sum(k=0, n, prime(k+1)*x^k);

solve(x=-0.9967, -0.9966, P(2436, x))

CROSSREFS

Cf. A346442, A346443, A346445, A346663.

KEYWORD

nonn,cons

AUTHOR

Hugo Pfoertner, Jul 18 2021

STATUS

approved

A346445

Decimal expansion, negated, of the greater real root of the polynomial of A346442.

+20
4

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

See A346442 for more information and references.

LINKS

Table of n, a(n) for n=0..90.

PROG

(PARI) P(n, x) = sum(k=0, n, prime(k+1)*x^k);

solve(x=-0.9966, -0.9958, P(2436, x))

CROSSREFS

Cf. A346442, A346443, A346444, A346663.

KEYWORD

nonn,cons

AUTHOR

Hugo Pfoertner, Jul 18 2021

STATUS

approved

A346663

The number of nonreal roots of Sum_{k=0..n} prime(k+1)*x^k.

+10
4

0, 0, 2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, 50, 50, 52, 52, 54, 54, 56, 56, 58, 58, 60, 60, 62, 62, 64, 64, 66, 66, 68, 68, 70, 70, 72, 72

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

This agrees with A052928 until n = 2436. a(2436) = 2434 and A052928(2436) = 2436. For n >= 2436 we have a(n) = n-2 for n even and a(n) = n - 1 for n odd, for an as yet undetermined number of n. A052928(n) = n - (n mod 2) for all n. See the paper by W. Clark and M. Shattuck linked to below.

LINKS

Table of n, a(n) for n=0..73.

W. Edwin Clark and Mark Shattuck, The Integer Sequence Transform a --> b where b_n is the Number of Real Roots of the Polynomial a_0 + a_1 x + a_2 x^2 + ... + a_n x^n, arXiv:2107.05572 [math.CO], 2021.

Index entries for sequences which agree for a long time but are different

CROSSREFS

Cf. A052928, A346442, A346443, A346444, A346445.

KEYWORD

nonn

AUTHOR

W. Edwin Clark, Jul 27 2021

STATUS

approved

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