A377758 a(n) is the least i such that 2n-prime(i) is also a prime, where prime(i) is the i-th prime.

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, 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, 2, 2, 3, 4, 5, 5, 2, 2, 3, 4, 2, 3, 4, 2, 3, 2, 3

Offset: 2

Author

Michel Eduardo Beleza Yamagishi, Nov 06 2024

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A000040, A000720, A020481, A377972.

Programs

Maple

f:= proc(n) local i,p;
  p:= 1:
  for i from 1 do
    p:= nextprime(p);
    if isprime(2*n-p) then return i fi
  od
end proc:
map(f, [$2..100]); # Robert Israel, Nov 19 2024

Mathematica

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

PARI

a(n) = my(i=1); while (!isprime(2*n-prime(i)), i++); i; \\ Michel Marcus, Nov 06 2024

Python

from sympy import primerange, isprime
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

Formula

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