A187222 - OEIS

%I #18 Feb 24 2021 02:48:19

%S 3,7,23,31,47,71,191,311,367,503,607,967,1303,1367,1439,1471,1663,

%T 1871,2399,4951,5471,5623,6263,9431,10103,10271,10687,12119,12511,

%U 14431,14879,15647,21871,22111,22271,22807,23039,24223,24919

%N Gullwing primes: primes in the gullwing sequence A187220.

%H Nathaniel Johnston, <a href="/A187222/b187222.txt">Table of n, a(n) for n = 1..3406</a>

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%F A000040 INTERSECT A187220.

%t m = 200 (* number of gullwing terms *); s = (2*(x/((1-x)*(1 + 2*x))))*(1 + 2*x*Product[1 + x^(2^k-1) + 2*x^2^k, {k, 0, Ceiling[Log[2, m]]}]) + O[x]^(m-1); Select[CoefficientList[s, x] + 1, PrimeQ] (* _Jean-François Alcover_, Jul 23 2017 *)

%Y Cf. A000040, A139253, A187220.

%K nonn

%O 1,1

%A _Omar E. Pol_, Mar 09 2011, Mar 10 2011

%E More terms from _Nathaniel Johnston_, Mar 22 2011