A288477 a(n) = (2^49 - 2)*n/3 + 247371098957.

247371098957, 187897355572727, 375547340046497, 563197324520267, 750847308994037, 938497293467807, 1126147277941577, 1313797262415347, 1501447246889117, 1689097231362887, 1876747215836657, 2064397200310427, 2252047184784197, 2439697169257967

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

Cf. A076336.

Sequence in context: A132908 A271820 A204781 * A268846 A076254 A213689

Adjacent sequences: A288474 A288475 A288476 * A288478 A288479 A288480

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Jun 09 2017

Status

approved