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

Author

Arkadiusz Wesolowski, Jun 09 2017

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A076336.

Programs

GAP

List([0..15],n->(2^49-2)*n/3+247371098957); # Muniru A Asiru, Oct 01 2018

Magma

[(2^49-2)*n/3+247371098957: n in [0..13]];

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 *)
LinearRecurrence[{2,-1},{247371098957,187897355572727},20] (* Harvey P. Dale, Feb 22 2025 *)

PARI

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

Formula

G.f.: (247371098957 + 187402613374813*x)/(1 - x)^2.