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Number of points of the inner discrete Theodorus spiral on sheet S_n, n >= 1. First differences of A295339.
2

%I #24 Dec 18 2017 04:31:46

%S 15,37,56,76,95,115,136,154,175,194,214,234,254,273,293,313,332,352,

%T 372,392,411,432,450,471,490,511,529,550,569,590,608,629,648,668,688,

%U 708,727,747,767

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

%C 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.

%C For the inner discrete Theodorus spiral see the Waldvogel link.

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

%H Joerg Waldvogel, <a href="http://www.sam.math.ethz.ch/~joergw/Papers/theopaper.pdf">Analytic Continuation of the Theodorus Spiral</a>.

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

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

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

%K nonn

%O 1,1

%A _Wolfdieter Lang_, Dec 13 2017