A218057 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.

2, 5, 41, 593, 4513, 155593, 1166225, 72873665, 543046721, 53486784401, 397441609945, 56635031066257, 420155471749553, 81721424164605401, 605653678328814113, 154142360945389303553, 1141616971745015134465, 368180757129736563169825, 2725567350297911241532841

Offset: 0

Author

M. F. Hasler, Oct 19 2012

Keywords

• nonn

Comments

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

Examples

			The first values are 1^0+2^1/2, 1^2+2^3/2, 3^2+4^3/2, 3^4+4^5/2, ...
		

Programs

Maple

A052928 := proc(n)
        2*floor(n/2) ;
end proc:
A109613 := proc(n)
        1+2*floor(n/2) ;
end proc:
A218057 := proc(n)
        A109613(n)^A052928(n+1)+A052928(n+2)^A109613(n+1)/2 ;
end proc: # R. J. Mathar, Oct 26 2012

PARI

A218057(n)=my(b=n\2*2);(b+1)^(n=(n+1)\2*2)+(b+2)^(n+1)/2

Formula

A218057(n) = A109613(n)^A052928(n+1) + A052928(n+2)^A109613(n+1)/2.