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A200832 Primes of the form (2^k + k)*2^k + 1. 7

%I #25 Jun 07 2021 01:11:59

%S 7,89,4481,268664833,4398090551297,18014402133360641,

%T 5070602400913032447777310769153,

%U 5316911983139663632271651803156709377,102844034832575377634685573910878950656009052628932024900517889

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

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

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

%C (see A200823).

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

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

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

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

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

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

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

%H Henri Lifchitz, <a href="http://www.primenumbers.net/Henri/us/NouvP1us.htm">New forms of primes</a>

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

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

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

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 23 2011

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)