A114557 a(2n-1) = 2*(p-1) and a(2n) = p + 3, where p=prime(n).

2, 5, 4, 6, 8, 8, 12, 10, 20, 14, 24, 16, 32, 20, 36, 22, 44, 26, 56, 32, 60, 34, 72, 40, 80, 44, 84, 46, 92, 50, 104, 56, 116, 62, 120, 64, 132, 70, 140, 74, 144, 76, 156, 82, 164, 86, 176, 92, 192, 100, 200, 104, 204, 106, 212, 110, 216, 112, 224, 116, 252, 130, 260, 134

Offset: 1

Author

Roger L. Bagula, Feb 15 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Programs

Magma

[((3-(-1)^n)*NthPrime(Floor((n+1)/2)) + (1+5*(-1)^n))/2: n in [1..70]]; // G. C. Greubel, May 20 2019

Mathematica

Flatten[Table[Abs[Coefficient[Expand[(x+2)(x -(1 +Sqrt[Prime[n]]))*(x - (1 - Sqrt[Prime[n]]))], x, m]], {n, 1, 50}, {m, 0, 1}]]
With[{p = Prime[Floor[(n+1)/2]]}, Table[If[OddQ[n], 2*(p-1), p+3], {n, 1, 70}]] (* G. C. Greubel, May 20 2019 *)

PARI

{a(n) = ((3-(-1)^n)*prime(floor((n+1)/2)) + (1+5*(-1)^n))/2}; \\ G. C. Greubel, May 20 2019

Sage

[( (3-(-1)^n)*nth_prime(floor((n+1)/2))+ (1+5*(-1)^n))/2 for n in (1..70)] # G. C. Greubel, May 20 2019

Formula

a(2n-1) = A037168(n). a(2n) = A113935(n).

a(n) = ( (3 - (-1)^n)*prime(floor((n+1)/2)) + (1 + 5*(-1)^n) )/2. - G. C. Greubel, May 20 2019