A062301 Number of ways writing n-th prime as a sum of two primes.

0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Labos Elemer, Jul 05 2001

Keywords

• nonn

Comments

a(n) = 1 if and only if n is in A006512. - Robert Israel, Apr 04 2018

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..3000

Crossrefs

Equals A061358(A000040(n)).

Cf. A006512, A014092, A025584.

Programs

GAP

P:=Filtered([1..1000],IsPrime);; a:=List(List(List(P, i -> Partitions(i,2)), k -> Filtered(k, i -> IsPrime(i[1]) and IsPrime(i[2]))),Length); # Muniru A Asiru, Apr 05 2018

Maple

a:= n-> `if`(isprime(ithprime(n)-2), 1, 0):
seq(a(n), n=1..105);  # Alois P. Heinz, Oct 02 2020

Mathematica

Table[Sum[(PrimePi[Prime[n] - i] - PrimePi[Prime[n] - i - 1]) (PrimePi[i] - PrimePi[i - 1]), {i, Floor[Prime[n]/2]}], {n, 100}] (* Wesley Ivan Hurt, Apr 04 2018 *)

PARI

a(n) = isprime(prime(n) - 2) \\ David A. Corneth, Apr 04 2018

Extensions

Offset changed to 1 by David A. Corneth, Apr 04 2018