A189227 - OEIS

%I #27 Jun 01 2017 13:51:28

%S -11,61,157,181,349,373,397,421,541,661,709,733,829,853,877,997,1021,

%T 1069,1093,1213,1237,1381,1429,1597,1621,1669,1693,1741,1861,2029,

%U 2221,2293,2341,2389,2557,2677,2749,2917,3037,3061,3109,3181,3229,3253,3301,3373

%N Primes among the curvatures in the nickel-dime-quarter Apollonian circle packing A189226.

%C See A189226 for comments, references, links, examples, and crossrefs.

%H Giovanni Resta, <a href="/A189227/b189227.txt">Table of n, a(n) for n = 1..1128</a> terms < 10^5.

%H S. Finch, <a href="/A189227/a189227.pdf">Apollonian circles with integer curvatures</a> [Cached copy, with permission of the author]

%F a(n) == 13 (mod 24) (because a(n) is prime, a(n) = A189226(k) for some k, and all terms of A189226 are == 0, 4, 12, 13, 16, or 21 (mod 24)).

%t (* terms < 10^4 *) t = Range[9999]*0; w = {-11, 21, 24, 28}; s[1] = {{-1,2,2,2}, {0,1,0,0}, {0,0,1,0}, {0,0,0,1}}; s[2] = {{1,0,0,0}, {2,-1,2,2}, {0,0,1,0}, {0,0,0,1}}; s[3] = {{1,0,0,0}, {0,1,0,0}, {2,2,-1,2}, {0,0,0,1}}; s[4] = {{1,0,0,0}, {0,1,0,0}, {0,0,1,0}, {2,2,2,-1}}; r[m_, j_, p_] := Block[{v = (m.w)[[p]]}, If[v < 9999, t[[v]] = 1; Do[ If[i != j, r[m.s[i], i, p]], {i, 4}]]]; Do[ r[s[i], i, i], {i, 4}]; Prepend[ Select[ Flatten@ Position[t,1], PrimeQ], -11] (* _Giovanni Resta_, Jan 02 2014 *)

%Y Cf. A248930, A248938.

%K sign

%O 1,1

%A _Jonathan Sondow_, Apr 22 2011

%E Corrected and extended by _Steven Finch_, Jan 02 2014

%E a(16)-a(46) from _Giovanni Resta_, Jan 02 2014