OFFSET
0,1
COMMENTS
For all n, the numbers a(n) and a(n) + 2 form a pair of consecutive Riesel numbers.
Conjecture: a(0) + 1 = 444813635232 is the smallest nonnegative even number m such that for all k >= 1 the absolute values of the numbers m - 2^k + 1 and m - 2^k - 1 are composite.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Carlos Rivera, Collection 20th - 019
Wikipedia, Riesel number
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(n) = (2^49 - 2)*n/3 + 444813635231.
G.f.: (444813635231 + 187205170838539*x)/(1 - x)^2.
From Colin Barker, Jun 25 2017: (Start)
a(n) = 7*(63544805033 + 26807140639110*n).
a(n) = 2*a(n-1) - a(n-2) for n>1.
(End)
MAPLE
seq(coeff(series((444813635231+187205170838539*x)/(1-x)^2, x, n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 01 2018
MATHEMATICA
Table[(2^49 - 2) n/3 + 444813635231, {n, 0, 13}] (* or *)
CoefficientList[Series[(444813635231 + 187205170838539 x)/(1 - x)^2, {x, 0, 13}], x]
PROG
(Magma) [(2^49-2)*n/3+444813635231: n in [0..13]];
(PARI) a(n)=(2^49-2)*n/3+444813635231
(PARI) Vec(7*(63544805033 + 26743595834077*x) / (1 - x)^2 + O(x^15)) \\ Colin Barker, Jun 25 2017
(GAP) List([0..15], n->(2^49-2)*n/3+444813635231); # Muniru A Asiru, Oct 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Arkadiusz Wesolowski, Jun 24 2017
STATUS
approved