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
Examples
. 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].
Links
- Reinhard Zumkeller, Rows n = 1..41 of triangle, flattened
Programs
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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
Comments