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
Offset: 0
Examples
-0.9966435137376729278202858884333768134513389514151775806...
Links
- 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.
Programs
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PARI
P(m,x)=sum(k=0,m,prime(k+1)*x^k); d(m,y)=derivnum(x=y,P(m,x)); solve(x=-0.9967,-0.9966,d(2436,x))