A377758 - OEIS

%I #24 Nov 20 2024 07:18:24

%S 1,2,2,2,3,2,2,3,2,2,3,2,3,4,2,2,3,4,2,3,2,2,3,2,3,4,2,3,4,2,2,3,4,2,

%T 3,2,2,3,4,2,3,2,3,4,2,3,4,8,2,3,2,2,3,2,2,3,2,3,4,6,5,6,8,2,3,2,3,4,

%U 2,2,3,4,5,5,2,2,3,4,2,3,4,2,3,2,3

%N a(n) is the least i such that 2n-prime(i) is also a prime, where prime(i) is the i-th prime.

%H Robert Israel, <a href="/A377758/b377758.txt">Table of n, a(n) for n = 2..10000</a>

%F a(n) = pi(A020481(n)).

%p f:= proc(n) local i,p;

%p   p:= 1:

%p   for i from 1 do

%p     p:= nextprime(p);

%p     if isprime(2*n-p) then return i fi

%p   od

%p end proc:

%p map(f, [$2..100]); # _Robert Israel_, Nov 19 2024

%t Table[Module[{i = 1}, While[i <= PrimePi[n] && ! PrimeQ[n - Prime[i]], i++]; If[i <= PrimePi[n], i, None]], {n, 4, 1000, 2}]

%o (PARI) a(n) = my(i=1); while (!isprime(2*n-prime(i)), i++); i; \\ _Michel Marcus_, Nov 06 2024

%o (Python)

%o from sympy import primerange, isprime

%o def A377758(n): return next(i for i, p in enumerate(primerange(2*n),1) if isprime((n<<1)-p)) # _Chai Wah Wu_, Nov 19 2024

%Y Cf. A000040, A000720, A020481, A377972.

%K nonn

%O 2,2

%A _Michel Eduardo Beleza Yamagishi_, Nov 06 2024