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A224075 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.

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