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A338467 a(n+1) = prime(n) + 2*n - a(n). a(1) = 1.

%I A338467 #31 Feb 03 2021 23:38:56
%S A338467 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 A338467 70,77,76,81,82,85,88,101,94,109,98,121,102,129,110,135,118,143,122,
%U A338467 155,126,161,130,175,144,181,148,187,156,191,168,199,176,207,180,215
%N A338467 a(n+1) = prime(n) + 2*n - a(n). a(1) = 1.
%F A338467 a(n+1) = A078916(n) - a(n). - _Michel Marcus_, Jan 31 2021
%e A338467 a(1) + a(2) - 2*1 = 1st prime; 1 + 3 - 2*1 = 2.
%e A338467 a(13) + a(14) - 2*13 = 13th prime; 32 + 35 - 2*13 = 41.
%p A338467 a:= proc(n) option remember; `if`(n=1, 1,
%p A338467       ithprime(n-1)-a(n-1)+2*n-2)
%p A338467     end:
%p A338467 seq(a(n), n=1..60);  # _Alois P. Heinz_, Jan 31 2021
%t A338467 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 A338467 (Python)
%o A338467 from sympy import prime
%o A338467 S=[1]
%o A338467 nomb=100
%o A338467 for n in range(1,nomb):
%o A338467     derterm=S[-1]
%o A338467     terme= prime(n)-derterm+2*(len(S))
%o A338467     S.append(terme)
%o A338467 print(S)
%o A338467 (PARI) a(n) = if (n==1, 1, prime(n-1) + 2*(n-1) - a(n-1)); \\ _Michel Marcus_, Jan 31 2021
%Y A338467 Cf. A000040, A001223, A036467, A078916.
%K A338467 nonn,easy
%O A338467 1,2
%A A338467 _Carole Dubois_, Jan 31 2021