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A248877
a(1) = 23, a(2) = 71, a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
1
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.
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
KEYWORD
nonn,easy
AUTHOR
Zeid Ghalyoun, Mar 05 2015
STATUS
approved