A354973 - OEIS

%I #32 Jul 07 2022 02:23:41

%S 0,1,2,4,8,9,18,19,38,39,40,41,82,83,166,167,168,169,338,339,678,679,

%T 680,681,1362,1363,1364,1365,1366,1367,2734,2735,5470,5471,5472,5473,

%U 5474,5475,10950,10951,10952,10953,21906,21907,43814,43815,43816,43817,87634

%N a(0)=0; for n > 0, a(n) = 2*a(n-1) if n-1 is prime, a(n-1) + 1 otherwise.

%F a(n) = A110299(k) - 2^k + n + 1, where k = primepi(n-1) and taking A110299(0) = 0. - _Kevin Ryde_, Jun 22 2022

%e 5 is prime, so a(6) = 2*a(5) = 2*9 = 18.

%e 6 is not prime, so a(7) = a(6) + 1 = 18 + 1 = 19.

%t a[0] = 0; a[n_] := a[n] = If[PrimeQ[n - 1], 2*a[n - 1], a[n - 1] + 1]; Array[a, 50, 0] (* _Amiram Eldar_, Jun 21 2022 *)

%o (Python)

%o from sympy import isprime

%o a = [0]; [a.append(2*a[-1] if isprime(n) else a[-1]+1) for n in range(48)]

%o print(a) # _Michael S. Branicky_, Jun 21 2022

%o (PARI) a(n) = my(k=primepi(n-1)); fromdigits(primes(k),2) - 1<<k + n + 1; \\ _Kevin Ryde_, Jun 22 2022

%Y Cf. A110299.

%K nonn

%O 0,3

%A _Ben White_, Jun 14 2022