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

0,1

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

Links

Table of n, a(n) for n=0..18.

Formula

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

Example

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

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

Prog

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

Crossrefs

Sequence in context: A088547 A009457 A175172 * A126469 A093433 A054859

Adjacent sequences: A218054 A218055 A218056 * A218058 A218059 A218060

Keyword

nonn

Author

M. F. Hasler, Oct 19 2012

Status

approved