cp's OEIS Frontend

A187733 Primes of the form 2^n + n + 2.

%I A187733 #29 Jul 24 2019 22:45:53
%S A187733 3,5,13,137,523,524309,134217757,8589934627,
%T A187733 178405961588244985132285746181186892047843477
%N A187733 Primes of the form 2^n + n + 2.
%C A187733 The list of associated n is: 0, 1, 3, 7, 9, 19, 27, 33, 147, 639, ...
%C A187733 Primes from A052968 of the form 2^(n-1) + n + 1 for n = 1, 2, 4, 8, 10, 20, 28, 34, ...
%C A187733 Pairs of twin primes of forms (2^n+n; 2^n+n+2): (3; 5), (11; 13), (521; 523), ...
%C A187733 The prime number a(10) = 2^639 + 639 + 2 has 193 digits.
%C A187733 a(11) = 2^12243 + 12243 + 2 and a(12) = 2^41427 + 41427 + 2. - _Giovanni Resta_, Jan 23 2013
%C A187733 The sequence contains the subsequence 13, 137, 524309,... where the n themselves are prime, n = 3, 7, 19 (no further up to 41427). - _Jaroslav Krizek_, Feb 27 2013
%H A187733 Hugo Pfoertner, <a href="/A187733/b187733.txt">Table of n, a(n) for n = 1..10</a>
%H A187733 FactorDB, <a href="http://factordb.com/index.php?query=2%5En+%2B+n+%2B+2&amp;use=n&amp;n=1&amp;VP=on&amp;VC=on&amp;EV=on&amp;OD=on&amp;PR=on&amp;FF=on&amp;PRP=on&amp;CF=on&amp;U=on&amp;C=on&amp;perpage=200&amp;format=1">2^n + n + 2</a>.
%e A187733 8589934627 is in the sequence since 8589934627 =  2^33 + 33 + 2 and 8589934627 is prime.
%t A187733 Select[Table[2^n + n + 2, {n, 60}], PrimeQ[#] &]
%Y A187733 Cf. A052968, A129962, A309328.
%K A187733 nonn
%O A187733 1,1
%A A187733 _Jaroslav Krizek_, Jan 19 2013