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%I #18 Jun 27 2017 19:02:22
%S 2,5,41,593,4513,155593,1166225,72873665,543046721,53486784401,
%T 397441609945,56635031066257,420155471749553,81721424164605401,
%U 605653678328814113,154142360945389303553,1141616971745015134465,368180757129736563169825,2725567350297911241532841
%N a(n) = (b(n)+1)^b(n+1) + b(n+2)^(b(n+1)+1)/2, where b(n) = [n/2]*2 = A052928(n) =(0,0,2,2,4,4,...), even numbers repeated.
%C Suggested by J. Gerasimov, based on the observation that the first 6 terms a(0)...a(5) are prime. The next primes in the sequence a(n) occur for n=12, 45, 65 and no other n below 1000. - _M. F. Hasler_, Oct 19 2012
%F A218057(n) = A109613(n)^A052928(n+1) + A052928(n+2)^A109613(n+1)/2.
%e The first values are 1^0+2^1/2, 1^2+2^3/2, 3^2+4^3/2, 3^4+4^5/2, ...
%p A052928 := proc(n)
%p 2*floor(n/2) ;
%p end proc:
%p A109613 := proc(n)
%p 1+2*floor(n/2) ;
%p end proc:
%p A218057 := proc(n)
%p A109613(n)^A052928(n+1)+A052928(n+2)^A109613(n+1)/2 ;
%p end proc: # _R. J. Mathar_, Oct 26 2012
%o (PARI) A218057(n)=my(b=n\2*2);(b+1)^(n=(n+1)\2*2)+(b+2)^(n+1)/2
%K nonn
%O 0,1
%A _M. F. Hasler_, Oct 19 2012
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