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A244365 Table read by rows: row n contains all primes p such that prime(n) < p <= floor(prime(n)^(1+1/n)).

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