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 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
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Length of n-th row = A105047(n+1); T(n,1) = A260485(n); T(n,A105047(n)) = A065091(n). 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 EXAMPLE 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 PROG (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 CROSSREFS Cf. A065305, A105047, A065091. Sequence in context: A138220 A137913 A137937 * A297468 A047565 A026466 Adjacent sequences: A260577 A260578 A260579 * A260581 A260582 A260583 KEYWORD nonn,tabf AUTHOR Reinhard Zumkeller, Aug 11 2015 STATUS approved

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Last modified May 25 16:17 EDT 2024. Contains 372801 sequences. (Running on oeis4.)