OFFSET
0,1
COMMENTS
For all n, the numbers a(n) and a(n) + 2 form a pair of consecutive Sierpiński numbers.
Conjecture: a(0) + 1 = 247371098958 is the smallest nonnegative even number m such that for all k >= 1 the numbers m + 2^k + 1 and m + 2^k - 1 are composite.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..5000
Carlos Rivera, Collection 20th - 019
Wikipedia, Sierpinski number
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: (247371098957 + 187402613374813*x)/(1 - x)^2.
MAPLE
seq(coeff(series((247371098957+187402613374813*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 + 247371098957, {n, 0, 13}] (* or *)
CoefficientList[Series[(247371098957 + 187402613374813 x)/(1 - x)^2, {x, 0, 13}], x] (* Michael De Vlieger, Jun 09 2017 *)
PROG
(Magma) [(2^49-2)*n/3+247371098957: n in [0..13]];
(PARI) a(n)=(2^49-2)*n/3+247371098957
(GAP) List([0..15], n->(2^49-2)*n/3+247371098957); # Muniru A Asiru, Oct 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Arkadiusz Wesolowski, Jun 09 2017
STATUS
approved