A260580 Table read by rows: n-th row contains numbers not occurring earlier, that can be written as (p+q)/2 where p is the n-th odd prime, q <= p.

3, 4, 5, 6, 7, 8, 9, 11, 10, 12, 13, 14, 15, 17, 16, 18, 19, 20, 21, 23, 24, 26, 29, 22, 25, 27, 30, 31, 28, 33, 34, 37, 32, 35, 36, 39, 41, 40, 42, 43, 38, 44, 45, 47, 48, 50, 53, 51, 56, 59, 46, 49, 52, 54, 57, 60, 61, 55, 63, 64, 67, 62, 65, 66, 69, 71

Offset: 1

Author

Reinhard Zumkeller, Aug 11 2015

Keywords

• nonn
• tabf

Comments

Length of n-th row = A105047(n+1);

T(n,1) = A260485(n);

T(n,A105047(n)) = A065091(n).

Examples

			Let p(n) = A065091(n) = prime(n+1):
.   n | p(n) | T(n,*)
. ----+------+----------------- ------------------------------------------
.   1 |    3 | [3]              3
.   2 |    5 | [4,5]            (5+3)/2,5
.   3 |    7 | [6,7]            (7+5)/2,7
.   4 |   11 | [8,9,11]         (11+5)/2,(11+7)/2,11
.   5 |   13 | [10,12,13]       (13+7)/2,(13+11)/2,13
.   6 |   17 | [14,15,17]       (17+11)/2,(17+13)/2,17
.   7 |   19 | [16,18,19]       (19+13)/2,(19+17)/2,19
.   8 |   23 | [20,21,23]       (23+17)/2,(23+19)/2,23
.   9 |   29 | [24,26,29]       (29+19)/2,(29+17)/2,29
.  10 |   31 | [22,25,27,30,31] (31+13)/2,(31+19)/2,(31+23)/2,(31+29)/2,31
.  11 |   37 | [28,33,34,37]    (37+19)/2,(37+29)/2,(37+31)/2,37
.  12 |   41 | [32,35,36,39,41] (41+23)/2,(41+29)/2,(41+31)/2,(41+37)/2,41
		

Links

• Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened
• Eric Weisstein's World of Mathematics, Goldbach Partition
• Wikipedia, Goldbach's conjecture
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A065305, A105047, A065091.

Programs

Haskell

import Data.List.Ordered (union); import Data.List ((\\))
a260580 n k = a260580_tabf !! (n-1) !! (k-1)
a260580_row n = a260580_tabf !! (n-1)
a260580_tabf = zipWith (\\) (tail zss) zss where
                            zss = scanl union [] a065305_tabl