%I #5 Mar 31 2013 15:46:32
%S 2,3,5,7,11,5,13,17,11,19,23,29,7,23,31,13,29,37,17,41,23,47,5,29,53,
%T 11,59,13,37,53,61,19,43,59,67,23,47,71,31,71,79,59,83,41,89,17,73,89,
%U 97,59,83,107,29,61,101,109,83,107,131,17,89,113,137,19,59
%N Triangle read by rows: n-th row gives the primes p of form (m - k^2) where m = A214583(n), k < m and gcd(k,m) = 1.
%C Defined where A214583 is defined.
%H Reinhard Zumkeller, <a href="/A224075/b224075.txt">Rows n = 1..41 of triangle, flattened</a>
%e . n | A214583 | T(n,k) for k = 1 .. A224076(n)
%e . ----+---------+-------------------------------------------------------
%e . 1 | 3 | [2]
%e . 2 | 4 | [3]
%e . 3 | 6 | [5]
%e . 4 | 8 | [7]
%e . 5 | 12 | [11]
%e . 6 | 14 | [5,13]
%e . 7 | 18 | [17]
%e . 8 | 20 | [11,19]
%e . 9 | 24 | [23]
%e . 10 | 30 | [29]
%e . 11 | 32 | [7,23,31] 32-5^2, 32-3^2, 32-1^2
%e . 12 | 38 | [13,29,37] 38-5^2, 38-3^2, 38-1^2
%e . 13 | 42 | [17,41] 42-5^2, 42-1^2
%e . 14 | 48 | [23,47] 48-5^2, 48-1^2
%e . 15 | 54 | [5,29,53] 54-7^2, 54-5^2, 54-1^2
%e . 16 | 60 | [11,59] 60-7^2, 60-1^2
%e . 17 | 62 | [13,37,53,61] 62-7^2, 62-5^2, 62-3^2, 62-1^2
%e . 18 | 68 | [19,43,59,67] 68-7^2, 68-5^2, 68-3^2, 68-1^2
%e . 19 | 72 | [23,47,71] 72-7^2, 72-5^2, 72-1^2
%e . 20 | 80 | [31,71,79] 80-7^2, 80-3^2, 80-1^2
%e . 21 | 84 | [59,83] 84-5^2, 83-1^2
%e . 22 | 90 | [41,89] 90-7^2, 90-1^2
%e . 23 | 98 | [17,73,89,97] 98-9^2, 98-5^2, 98-3^2, 98-1^2
%e . 24 | 108 | [59,83,107] 108-7^2, 108-5^2, 108-1^2
%e . 25 | 110 | [29,61,101,109] 110-9^2, 110-7^2, 101-3^2, 101-1^2
%e . 26 | 132 | [83,107,131] 132-7^2, 132-5^2, 132-1^2
%e . 27 | 138 | [17,89,113,137] 138-11^2, 138-7^2, ...
%e . 28 | 140 | [19,59,131,139] ...
%e . 29 | 150 | [29,101,149]
%e . 30 | 180 | [11,59,131,179]
%e . 31 | 182 | [61,101,157,173,181]
%e . 32 | 198 | [29,149,173,197]
%e . 33 | 252 | [83,131,227,251]
%e . 34 | 318 | [29,149,197,269,293,317]
%e . 35 | 360 | [71,191,239,311,359]
%e . 36 | 398 | [37,109,173,229,277,317,349,373,389,397]
%e . 37 | 468 | [107,179,347,419,443,467]
%e . 38 | 570 | [41,281,401,449,521,569]
%e . 39 | 572 | [43,131,211,283,347,491,523,547,563,571]
%e . 40 | 930 | [89,401,569,641,761,809,881,929]
%e . 41 | 1722 | [353,761,881,1097,1193,1361,1433,1553,1601,1697,1721].
%o (Haskell)
%o a224075 n k = a224075_tabf !! (n-1) !! (k-1)
%o a224075_row n = a224075_tabf !! (n-1)
%o a224075_tabf = f 3 where
%o f x = g [] 3 1 where
%o g ps i k2 | x <= k2 = ps : f (x + 1)
%o | gcd k2 x > 1 = g ps (i + 2) (k2 + i)
%o | a010051 q == 1 = g (q:ps) (i + 2) (k2 + i)
%o | otherwise = f (x + 1)
%o where q = x - k2
%Y Cf. A224076 (row lengths), A010051.
%K nonn,tabf
%O 1,1
%A _Reinhard Zumkeller_, Mar 31 2013