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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A093125 A226390 A156081 * A089881 A251547 A084320

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

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Last modified September 20 12:32 EDT 2019. Contains 327235 sequences. (Running on oeis4.)