A200832 Primes of the form (2^k + k)*2^k + 1.

7, 89, 4481, 268664833, 4398090551297, 18014402133360641, 5070602400913032447777310769153, 5316911983139663632271651803156709377, 102844034832575377634685573910878950656009052628932024900517889

Offset

1,1

Comments

The generalization of this sequence is possible with the primes of the form (b^n +- k)*b^n +- 1.

The corresponding indices k are 1, 3, 6, 14, 21, 27, 51, 61, 103, 123, 126, 414, 499, 1509, 2389, ...

(see A200823).

For k = 103, a(9) has 63 digits;

for k = 123, a(10) has 75 digits;

for k = 126, a(11) has 76 digits;

for k = 414, a(12) has 250 digits;

for k = 499, a(13) has 301 digits;

for k = 1509, a(14) has 909 digits;

for k = 2389, a(15) has 1439 digits.

Links

Table of n, a(n) for n=1..9.

Henri Lifchitz, New forms of primes

Example

89 is in the sequence because, for k = 3, (2^3 + 3)*2^3 + 1 = 89 is prime.

Mathematica

a={}; Do[p=(2^n + n)*2^n+1; If[PrimeQ[p], AppendTo[a, p]], {n, 10^3}]; Print[a];

Crossrefs

Cf. A200816, A200817, A200818, A200819, A200821, A200822, A200823.

Sequence in context: A099719 A142995 A350937 * A103064 A244849 A355591

Adjacent sequences: A200829 A200830 A200831 * A200833 A200834 A200835

Keyword

nonn

Author

Michel Lagneau, Nov 23 2011

Status

approved