A323492 Indices of the sign changes of the sequence c(n) satisfying Sum_{k=0..n} c(k)/(n+k+1) = 0 with c(0)=1.

0, 1, 26, 532, 10457

Offset

1,3

Links

Table of n, a(n) for n=1..5.

Alexander Kalmynin, Petr Kosenko, Orthorecursive expansion of unity, arXiv:1901.04044 [math.NT], 2019.

Example

c(0)=1 and c(1)=-3/2, so the 1st sign change is at n=0, a(1) = 0.
c(1)=-3/2 and c(2)=5/24, so the 2nd sign change is at n=1, a(2) = 1.

Prog

(PARI) lista(nn) = {my(c0 = 1., vc = vector(nn), s = 1); for (n=1, nn, vc[n] = -(2*n+1)*(c0/(n+1) + sum(k=1, n-1, vc[k]/(n+k+1))); if (sign(vc[n]*s) < 0, print1(n-1, ", ")); s = sign(vc[n]); ); }

Crossrefs

Cf. A323490 (numerators of c(n)).

Sequence in context: A205990 A230247 A058461 * A265461 A257518 A283343

Adjacent sequences: A323489 A323490 A323491 * A323493 A323494 A323495

Keyword

nonn,more

Author

Michel Marcus, Jan 16 2019

Status

approved