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A200822
Primes of the form (2^k + k)*2^k - 1.
7
5, 23, 295147905763468378111, 26328072917139296674479506920934969822344499680020176660678574079
OFFSET
1,1
COMMENTS
The corresponding indices k are 1, 2, 34, 107, 1568, 1933, 3551, 6793, ... (see A200821).
The generalization of this sequence is possible with the primes of the form (b^n +- k)*b^n +- 1.
For k = 107, a(4) has 65 digits;
for k = 1568, a(5) has 945 digits;
for k = 1933, a(6) has 1164 digits;
for k = 3551, a(7) has 2138 digits;
for k = 6793, a(8) has 4090 digits.
EXAMPLE
23 is in the sequence because, for k=2, (2^2 + 2)*2^2 - 1 = 23 is prime.
MATHEMATICA
a={}; Do[p=(2^n + n)*2^n-1; If[PrimeQ[p], AppendTo[a, p]], {n, 10^3}]; Print[a]
Select[Table[(2^n+n)2^n-1, {n, 200}], PrimeQ] (* Harvey P. Dale, Dec 18 2015 *)
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 23 2011
STATUS
approved