A105047 Form an addition table of the primes; a(n) is the number of even numbers that appear for the first time in column n.

1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 5, 4, 5, 3, 4, 3, 3, 7, 4, 5, 4, 3, 5, 5, 6, 5, 5, 4, 4, 3, 7, 5, 5, 7, 5, 5, 6, 4, 6, 5, 5, 7, 4, 6, 5, 4, 6, 5, 8, 5, 7, 4, 5, 6, 5, 3, 3, 8, 8, 5, 4, 5, 8, 8, 5, 5, 9, 4, 8, 7, 7, 6, 6, 5, 5, 7, 5, 7, 7, 6, 6, 6, 6, 5, 7, 7, 6, 6, 5, 6, 5, 5, 7, 4, 8, 4, 8, 5, 8, 7, 8, 9, 7, 5, 9

Offset: 1

Author

Andrew S. Plewe, Apr 06 2005

Keywords

• nonn

Comments

For n > 2: a(n) = A102696(n-1) - A102696(n-2); a(n+1) = length of n-th row in the triangle A260580. - Reinhard Zumkeller, Aug 11 2015

Examples

			The addition table is as follows:
   + | 2  3  5  7 11
   --+--------------
   2 | 4  5  7  9 13
   3 |    6  8 10 14
   5 |      10 12 16
   7 |         14 18
  11 |            22
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Goldbach Partition
• Wikipedia, Goldbach's conjecture
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A102696, A260580.

Programs

Haskell

a105047 1 = 1
a105047 n = length $ a260580_row (n - 1)
-- Reinhard Zumkeller, Aug 11 2015

PARI

lista(n) = {maxp = prime(n); v = vector(maxp); forprime (p=1, maxp, nb = 0; forprime (q=1, p, s = p+q; if (! (s % 2), if (!v[s/2], nb++); v[s/2] = 1;);); print1(nb, ", "););}  \\ Michel Marcus, Apr 18 2013

Extensions

More terms from Reinhard Zumkeller, Apr 19 2005