A071635 Number of decompositions of 4*n+2 into sum of two primes of form 4*k+1.

0, 0, 1, 0, 1, 1, 1, 1, 2, 0, 2, 2, 1, 2, 3, 0, 3, 2, 2, 3, 2, 1, 3, 2, 1, 4, 3, 2, 5, 3, 2, 5, 3, 2, 3, 4, 2, 5, 4, 1, 5, 3, 3, 4, 4, 1, 6, 4, 3, 6, 5, 2, 9, 3, 3, 4, 4, 2, 6, 4, 2, 8, 4, 4, 5, 4, 3, 8, 5, 2, 7, 7, 4, 9, 6, 3, 7, 6, 3, 6, 6, 2, 12, 5, 4, 8, 6, 5, 10, 4, 2, 10, 7, 4

Offset: 0

Author

Reinhard Zumkeller, May 27 2002

Keywords

• nonn
• look

Comments

For a(m)=0 see A071636.

Examples

			a(10)=2 as 4*10+2 = 42 = 5+37 = (4*1+1)+(4*9+1) = 13+29 = (4*3+1)+(4*7+1) and the other two decompositions 42 = 11+31 = (4*2+3)+(4*7+3) = 19+23 = (4*4+3)+(4*5+3), A002375(21)=4.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to Goldbach conjecture.

Crossrefs

Cf. A002375, A002144, A071636, A156642.

Programs

Mathematica

a[n_] := Module[{s = 0}, For[p = 3, p <= 2n+1, p = NextPrime[p], If[Mod[p, 4] == 1 && PrimeQ[4n+2-p], s++]]; s];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 17 2021, after Andrew Howroyd *)

PARI

a(n)={my(s=0); forprime(p=3, 2*n+1, if(p%4==1 && isprime(4*n+2-p), s++)); s} \\ Andrew Howroyd, Feb 02 2020

Formula

a(n) = A002375(2*n+1) - A156642(n). - Vladimir Shevelev, Feb 12 2009