A296179 Number of points of the inner discrete Theodorus spiral on sheet S_n, n >= 1. First differences of A295339.

15, 37, 56, 76, 95, 115, 136, 154, 175, 194, 214, 234, 254, 273, 293, 313, 332, 352, 372, 392, 411, 432, 450, 471, 490, 511, 529, 550, 569, 590, 608, 629, 648, 668, 688, 708, 727, 747, 767

Offset

1,1

Comments

In the complex plane the punctured sheets S_n are given by rho*exp(i*phi_n), with rho > 0 and 2*Pi*(n-1) <= phi_n < 2*Pi*n, for n >= 1.

For the inner discrete Theodorus spiral see the Waldvogel link.

The conjecture stated in A295339 implies that a(n) = A295338(n), for n >= 2.

Links

Table of n, a(n) for n=1..39.

Joerg Waldvogel, Analytic Continuation of the Theodorus Spiral.

Formula

a(n) = b(n) - b(n-1), for n >= 1, with b(n) = A295339(n), and b(0) = 0.

Conjecture: a(n) = A295338(n), for n >= 2 (see a comment above).

Crossrefs

Cf. A295339, A295338 (outer spiral), A172164.

Sequence in context: A329909 A118867 A260796 * A181362 A082112 A059605

Adjacent sequences: A296176 A296177 A296178 * A296180 A296181 A296182

Keyword

nonn

Author

Wolfdieter Lang, Dec 13 2017

Status

approved