A292041 - OEIS

%I #31 Feb 16 2025 08:33:51

%S 14,219,3243,48002,710534,10517258,155675283,2304288003,34107811455,

%T 504859983098,7472880600122,110612736864003,1637277271142775,

%U 24234793737149739,358720686980681762,5309743200769920002,78594220744343904494,1163342802249829489179

%N a(n) = floor(c^n) where c = (2^(1/3)-1)^(-2) = 14.801887...(n > 0).

%C All the numbers in this sequence are composites. The sequence was discovered by M. N. Huxley and published in the paper by Baker and Harman.

%C Each term == 2 or 3 (mod 6). - _Robert Israel_, Sep 08 2017

%H Robert Israel, <a href="/A292041/b292041.txt">Table of n, a(n) for n = 1..853</a>

%H Roger C. Baker and Glyn Harman, <a href="http://eudml.org/doc/174835">Primes of the form [c^p]</a>, Mathematische Zeitschrift, Vol. 221, No. 1 (1996), pp. 73-81.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimefreeSequence.html">Primefree Sequence</a>.

%p Digits:= 1000:

%p c:=  (2^(1/3)-1)^(-2):

%p seq(floor(c^n),n=1..50); # _Robert Israel_, Sep 08 2017

%t c = (2^(1/3) - 1)^(-2); Table[Floor[c^n], {n, 1, 10}]

%o (PARI) a(n) = floor(1/(2^(1/3)-1)^(2*n)); \\ _Altug Alkan_, Sep 08 2017

%K nonn,changed

%O 1,1

%A _Amiram Eldar_, Sep 08 2017