A346442 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A346442

Decimal expansion, negated, of the location of the first occurrence of a negative minimum of the function P(x,m) = Sum_{k=1..m} prime(k)*x^(k-1), with m chosen such that P(x) has 2 real zeros, which occurs for m = 2436. The corresponding function value is A346443.

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

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

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..95.

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.

Mathematics Stack Exchange, An interesting observation on the roots of certain polynomials, March 2021.

User "Linear Christmas" in Stack Exchange comments, Graph of P(x,2436), Mar 18 2021.

EXAMPLE

-0.9966435137376729278202858884333768134513389514151775806...

PROG

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