A105047 - OEIS

%I #20 Oct 13 2018 09:13:57

%S 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,

%T 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,

%U 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

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

%C 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

%H Reinhard Zumkeller, <a href="/A105047/b105047.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbachPartition.html">Goldbach Partition</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%e The addition table is as follows:

%e    + | 2  3  5  7 11

%e    --+--------------

%e    2 | 4  5  7  9 13

%e    3 |    6  8 10 14

%e    5 |      10 12 16

%e    7 |         14 18

%e   11 |            22

%o (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

%o (Haskell)

%o a105047 1 = 1

%o a105047 n = length $ a260580_row (n - 1)

%o -- _Reinhard Zumkeller_, Aug 11 2015

%Y Cf. A102696, A260580.

%K nonn

%O 1,3

%A _Andrew S. Plewe_, Apr 06 2005

%E More terms from _Reinhard Zumkeller_, Apr 19 2005