A082454 a(n) = prime(n) + prime(n-1) - a(n-1) with a(0) = a(1) = 0.

0, 0, 5, 3, 9, 9, 15, 15, 21, 21, 31, 29, 39, 39, 45, 45, 55, 57, 63, 65, 73, 71, 81, 81, 91, 95, 103, 101, 109, 107, 115, 125, 133, 135, 141, 147, 153, 155, 165, 165, 175, 177, 183, 189, 195, 195, 201, 209, 225, 225, 231, 231, 241, 239, 253, 255, 265, 267, 273, 275

Offset: 0

Author

Labos Elemer, Apr 25 2003

Keywords

• nonn

Comments

In fact only one initial value is needed.

If initial values were {a(0)=0, a(1)=1} then we would get A014687.

prime(10) + prime(11) = 29 + 31 = a(10) + a(11) = 31 + 29 (order was reversed!).

If initial values were {a(0)=1, a(1)=2} then (after a(0)=1) we would get A000040, the primes, and would have prime(10) + prime(11) = 29 + 31 = a(10) + a(11) = 29 + 31 (identity).

Initial values {a(0)=1, a(1)=3} would give A014686.

Crossrefs

Cf. A000040, A014686, A014687, A082455.

Programs

Mathematica

g[x_] := Prime[x]+Prime[x-1]-g[x-1] g[0]=0; g[1]=0; Table[g[w], {w, 0, 100}]
Prepend[Table[Prime[n] + 2 (-1)^n, {n, 59}],0] (* George Beck, Jun 03 2022 *)

PARI

lista(nn) = {print1(a=0, ", "); print1(a, ", "); for (n=2, nn, a = prime(n) + prime(n-1) - a; print1(a, ", "););} \\ Michel Marcus, Apr 06 2015

Formula

a(n) = prime(n) + 2*(-1)^n. - George Beck, Jun 03 2022

Extensions

Name corrected by George Beck, Jun 03 2022