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%I #14 Jan 24 2022 08:47:37
%S 3,5,7,11,13,17,17,19,19,23,23,29,31,31,37,37,41,41,43,47,43,47,53,47,
%T 53,53,59,59,61,67,61,67,71,73,67,71,73,71,73,79,83,73,79,83,79,83,89,
%U 83,89,89,97,97,101,103,107,101,103,107,109,113,103,107,109
%N Table read by rows: row n contains all primes p such that prime(n) < p <= floor(prime(n)^(1+1/n)).
%C Length of n-th row = A182134(n);
%C T(n,1) = A000040(n+1); T(n,A182134(n)) = A245396(n).
%H Reinhard Zumkeller, <a href="/A244365/b244365.txt">Rows n = 1..1000 of triangle, flattened</a>
%F T(n,k) = A000040(n+k) for k = 1 .. A182134(n).
%e . n | A182134(n) | A249669(n) | T(n,1) ... T(n,A182134(n))
%e . ----+------------+------------+----------------------------
%e . 1 | 1 | 4 | [3]
%e . 2 | 1 | 5 | [5]
%e . 3 | 1 | 8 | [7]
%e . 4 | 1 | 11 | [11]
%e . 5 | 2 | 17 | [13, 17]
%e . 6 | 2 | 19 | [17, 19]
%e . 7 | 2 | 25 | [19, 23]
%e . 8 | 1 | 27 | [23]
%e . 9 | 2 | 32 | [29, 31]
%e . 10 | 2 | 40 | [31, 37]
%e . 11 | 2 | 42 | [37, 41]
%e . 12 | 3 | 49 | [41, 43, 47]
%e . 13 | 3 | 54 | [43, 47, 53]
%e . 14 | 2 | 56 | [47, 53]
%e . 15 | 2 | 60 | [53, 59]
%e . 16 | 3 | 67 | [59, 61, 67]
%e . 17 | 4 | 74 | [61, 67, 71, 73]
%e . 18 | 3 | 76 | [67, 71, 73]
%e . 19 | 4 | 83 | [71, 73, 79, 83]
%e . 20 | 3 | 87 | [73, 79, 83]
%e . 21 | 3 | 89 | [79, 83, 89]
%e . 22 | 2 | 96 | [83, 89]
%e . 23 | 2 | 100 | [89, 97]
%e . 24 | 4 | 107 | [97, 101, 103, 107]
%e . 25 | 5 | 116 | [101, 103, 107, 109, 113] .
%o (Haskell)
%o a244365 n k = a244365_tabf !! (n-1) !! (k-1)
%o a244365_row n = a244365_tabf !! (n-1)
%o a244365_tabf = zipWith farideh (map (+ 1) a000040_list) a249669_list
%o where farideh u v = filter ((== 1) . a010051') [u..v]
%o (PARI) row(n) = my(list=List(), p=prime(n)); forprime(q=nextprime(p+1), p^(1+1/n), listput(list, q)); Vec(list); \\ _Michel Marcus_, Jan 24 2022
%Y Cf. A182134 (row lengths), A245722 (row products), A245396, A249669, A010051, A000040.
%K nonn,tabf
%O 1,1
%A _Reinhard Zumkeller_, Nov 16 2014
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