A248877 a(1) = 23, a(2) = 71, a(n) = 3*a(n-1) - 2*a(n-2) for n>2.

23, 71, 167, 359, 743, 1511, 3047, 6119, 12263, 24551, 49127, 98279, 196583, 393191, 786407, 1572839, 3145703, 6291431, 12582887, 25165799, 50331623, 100663271, 201326567, 402653159, 805306343, 1610612711, 3221225447, 6442450919, 12884901863, 25769803751

Offset

1,1

Comments

The first 6 terms are prime, so are the 9th, 10th, 13th, 14th, 15th, 18th, 20th, and 26th.

Any term of the form a(7+n*10) appears to be divisible by 11.

Any term of the form a(11+n*12) appears to be divisible by 13.

Any term of the form a(1+n*22) appears to be divisible by 23.

Any term that is not prime appears to have its factors recurring periodically in the sequence as factors of higher terms.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

a(n) = 3*2^(n+3)-25 = A007283(n+3)-25.

a(n+1) = a(n)+3*2^(n+3) with a(1) = 23.

a(n) = 3*a(n-1)-2*a(n-2). - Colin Barker, Mar 05 2015

G.f.: x*(2*x+23) / ((x-1)*(2*x-1)). - Colin Barker, Mar 05 2015

Mathematica

Table[3*2^(n + 3) - 25, {n, 1, k}]
LinearRecurrence[{3, -2}, {23, 71}, 30] (* Harvey P. Dale, Apr 10 2021 *)

Prog

(PARI) Vec(x*(2*x+23)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 05 2015
(Magma) [3*2^(n + 3) - 25: n in [1..30]]; // Vincenzo Librandi, Mar 08 2015

Crossrefs

Sequence in context: A154619 A142405 A139962 * A321356 A139878 A035072

Adjacent sequences: A248874 A248875 A248876 * A248878 A248879 A248880

Keyword

nonn,easy

Author

Zeid Ghalyoun, Mar 05 2015

Status

approved