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.

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, 11, 59, 13, 37, 53, 61, 19, 43, 59, 67, 23, 47, 71, 31, 71, 79, 59, 83, 41, 89, 17, 73, 89, 97, 59, 83, 107, 29, 61, 101, 109, 83, 107, 131, 17, 89, 113, 137, 19, 59

Offset

1,1

Comments

Defined where A214583 is defined.

Links

Reinhard Zumkeller, Rows n = 1..41 of triangle, flattened

Example

.   n | A214583 |  T(n,k) for k = 1 .. A224076(n)
. ----+---------+-------------------------------------------------------
.   1 |      3  |  [2]
.   2 |      4  |  [3]
.   3 |      6  |  [5]
.   4 |      8  |  [7]
.   5 |     12  |  [11]
.   6 |     14  |  [5,13]
.   7 |     18  |  [17]
.   8 |     20  |  [11,19]
.   9 |     24  |  [23]
.  10 |     30  |  [29]
.  11 |     32  |  [7,23,31]           32-5^2, 32-3^2, 32-1^2
.  12 |     38  |  [13,29,37]          38-5^2, 38-3^2, 38-1^2
.  13 |     42  |  [17,41]             42-5^2, 42-1^2
.  14 |     48  |  [23,47]             48-5^2, 48-1^2
.  15 |     54  |  [5,29,53]           54-7^2, 54-5^2, 54-1^2
.  16 |     60  |  [11,59]             60-7^2, 60-1^2
.  17 |     62  |  [13,37,53,61]       62-7^2, 62-5^2, 62-3^2, 62-1^2
.  18 |     68  |  [19,43,59,67]       68-7^2, 68-5^2, 68-3^2, 68-1^2
.  19 |     72  |  [23,47,71]          72-7^2, 72-5^2, 72-1^2
.  20 |     80  |  [31,71,79]          80-7^2, 80-3^2, 80-1^2
.  21 |     84  |  [59,83]             84-5^2, 83-1^2
.  22 |     90  |  [41,89]             90-7^2, 90-1^2
.  23 |     98  |  [17,73,89,97]       98-9^2, 98-5^2, 98-3^2, 98-1^2
.  24 |    108  |  [59,83,107]         108-7^2, 108-5^2, 108-1^2
.  25 |    110  |  [29,61,101,109]     110-9^2, 110-7^2, 101-3^2, 101-1^2
.  26 |    132  |  [83,107,131]        132-7^2, 132-5^2, 132-1^2
.  27 |    138  |  [17,89,113,137]     138-11^2, 138-7^2, ...
.  28 |    140  |  [19,59,131,139]     ...
.  29 |    150  |  [29,101,149]
.  30 |    180  |  [11,59,131,179]
.  31 |    182  |  [61,101,157,173,181]
.  32 |    198  |  [29,149,173,197]
.  33 |    252  |  [83,131,227,251]
.  34 |    318  |  [29,149,197,269,293,317]
.  35 |    360  |  [71,191,239,311,359]
.  36 |    398  |  [37,109,173,229,277,317,349,373,389,397]
.  37 |    468  |  [107,179,347,419,443,467]
.  38 |    570  |  [41,281,401,449,521,569]
.  39 |    572  |  [43,131,211,283,347,491,523,547,563,571]
.  40 |    930  |  [89,401,569,641,761,809,881,929]
.  41 |   1722  |  [353,761,881,1097,1193,1361,1433,1553,1601,1697,1721].

Prog

(Haskell)
a224075 n k = a224075_tabf !! (n-1) !! (k-1)
a224075_row n = a224075_tabf !! (n-1)
a224075_tabf = f 3 where
   f x = g [] 3 1 where
     g ps i k2 | x <= k2        = ps : f (x + 1)
               | gcd k2 x > 1   = g ps (i + 2) (k2 + i)
               | a010051 q == 1 = g (q:ps) (i + 2) (k2 + i)
               | otherwise      = f (x + 1)
               where q = x - k2

Crossrefs

Cf. A224076 (row lengths), A010051.

Sequence in context: A349872 A087174 A071963 * A354790 A053724 A046220

Adjacent sequences: A224072 A224073 A224074 * A224076 A224077 A224078

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Mar 31 2013

Status

approved