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

1,3

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

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

Example

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

Prog

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

Crossrefs

Cf. A102696, A260580.

Sequence in context: A156081 A368991 A147954 * A331135 A089881 A251547

Adjacent sequences: A105044 A105045 A105046 * A105048 A105049 A105050

Keyword

nonn

Author

Andrew S. Plewe, Apr 06 2005

Extensions

More terms from Reinhard Zumkeller, Apr 19 2005

Status

approved