A289111 a(n) = (2^49 - 2)*n/3 + 444813635231.

444813635231, 188094798109001, 375744782582771, 563394767056541, 751044751530311, 938694736004081, 1126344720477851, 1313994704951621, 1501644689425391, 1689294673899161, 1876944658372931, 2064594642846701, 2252244627320471, 2439894611794241

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

Cf. A101036.

Sequence in context: A082411 A113952 A218865 * A364785 A209833 A255578

Adjacent sequences: A289108 A289109 A289110 * A289112 A289113 A289114

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Jun 24 2017

Status

approved