A346663 The number of nonreal roots of Sum_{k=0..n} prime(k+1)*x^k.

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

Offset: 0

Author

W. Edwin Clark, Jul 27 2021

Keywords

• nonn

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

• 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.