A338467 - OEIS

%I #31 Feb 03 2021 23:38:56

%S 1,3,4,7,8,13,12,19,16,25,24,29,32,35,36,41,44,49,48,57,54,61,62,67,

%T 70,77,76,81,82,85,88,101,94,109,98,121,102,129,110,135,118,143,122,

%U 155,126,161,130,175,144,181,148,187,156,191,168,199,176,207,180,215

%N a(n+1) = prime(n) + 2*n - a(n). a(1) = 1.

%F a(n+1) = A078916(n) - a(n). - _Michel Marcus_, Jan 31 2021

%e a(1) + a(2) - 2*1 = 1st prime; 1 + 3 - 2*1 = 2.

%e a(13) + a(14) - 2*13 = 13th prime; 32 + 35 - 2*13 = 41.

%p a:= proc(n) option remember; `if`(n=1, 1,

%p       ithprime(n-1)-a(n-1)+2*n-2)

%p     end:

%p seq(a(n), n=1..60);  # _Alois P. Heinz_, Jan 31 2021

%t a[1] = 1; a[n_] := a[n] = Prime[n - 1] + 2*(n - 1) - a[n - 1]; Array[a, 60] (* _Amiram Eldar_, Feb 01 2021 *)

%o (Python)

%o from sympy import prime

%o S=[1]

%o nomb=100

%o for n in range(1,nomb):

%o     derterm=S[-1]

%o     terme= prime(n)-derterm+2*(len(S))

%o     S.append(terme)

%o print(S)

%o (PARI) a(n) = if (n==1, 1, prime(n-1) + 2*(n-1) - a(n-1)); \\ _Michel Marcus_, Jan 31 2021

%Y Cf. A000040, A001223, A036467, A078916.

%K nonn,easy

%O 1,2

%A _Carole Dubois_, Jan 31 2021