A377972 a(n) is the greatest i such that 2n-prime(i) is also a prime, where prime(i) is the i-th prime.

1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 11, 11, 11, 12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 22, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 30, 29, 30, 30, 29, 31, 31, 32

Offset

2,2

Links

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

Formula

a(n) = A000720(A020482(n)).

prime(a(n)) + prime(A377758(n)) = 2*n.

Example

For n=2, 2*2 - 2 = 2 and pi(2) = 1.
For n=3, 2*3 - 3 = 3, pi(3)=2.

Maple

P:= select(isprime, [2, seq(i, i=3..200, 2)]):
f:= proc(n) local m, j;
    m:= ListTools:-BinaryPlace(P, 2*n);
    for j from m to 1 by -1 do
      if isprime(2*n-P[j]) then return j fi
    od
end proc:
map(f, [$2..100]); # Robert Israel, Nov 16 2025

Mathematica

Table[Max[PrimePi[Flatten[Select[IntegerPartitions[2 n, {2}], AllTrue[#, PrimeQ] &]]]], {n, 2, 101}]

Prog

(PARI) a(n) = forprime(q=2, n, if(isprime(2*n-q), return(primepi(2*n-q)))); \\ Michel Marcus, Nov 16 2024

Crossrefs

Cf. A000040, A000720, A020482, A377758.

Sequence in context: A082288 A305397 A316627 * A099801 A099802 A196266

Adjacent sequences: A377969 A377970 A377971 * A377973 A377974 A377975

Keyword

nonn

Author

Michel Eduardo Beleza Yamagishi, Nov 13 2024

Status

approved