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

3, 5, 7, 11, 13, 17, 17, 19, 19, 23, 23, 29, 31, 31, 37, 37, 41, 41, 43, 47, 43, 47, 53, 47, 53, 53, 59, 59, 61, 67, 61, 67, 71, 73, 67, 71, 73, 71, 73, 79, 83, 73, 79, 83, 79, 83, 89, 83, 89, 89, 97, 97, 101, 103, 107, 101, 103, 107, 109, 113, 103, 107, 109

Offset: 1

Author

Reinhard Zumkeller, Nov 16 2014

Keywords

• nonn
• tabf

Comments

Length of n-th row = A182134(n);

T(n,1) = A000040(n+1); T(n,A182134(n)) = A245396(n).

Examples

			.   n | A182134(n) | A249669(n) |  T(n,1) ... T(n,A182134(n))
. ----+------------+------------+----------------------------
.   1 |          1 |          4 |  [3]
.   2 |          1 |          5 |  [5]
.   3 |          1 |          8 |  [7]
.   4 |          1 |         11 |  [11]
.   5 |          2 |         17 |  [13, 17]
.   6 |          2 |         19 |  [17, 19]
.   7 |          2 |         25 |  [19, 23]
.   8 |          1 |         27 |  [23]
.   9 |          2 |         32 |  [29, 31]
.  10 |          2 |         40 |  [31, 37]
.  11 |          2 |         42 |  [37, 41]
.  12 |          3 |         49 |  [41, 43, 47]
.  13 |          3 |         54 |  [43, 47, 53]
.  14 |          2 |         56 |  [47, 53]
.  15 |          2 |         60 |  [53, 59]
.  16 |          3 |         67 |  [59, 61, 67]
.  17 |          4 |         74 |  [61, 67, 71, 73]
.  18 |          3 |         76 |  [67, 71, 73]
.  19 |          4 |         83 |  [71, 73, 79, 83]
.  20 |          3 |         87 |  [73, 79, 83]
.  21 |          3 |         89 |  [79, 83, 89]
.  22 |          2 |         96 |  [83, 89]
.  23 |          2 |        100 |  [89, 97]
.  24 |          4 |        107 |  [97, 101, 103, 107]
.  25 |          5 |        116 |  [101, 103, 107, 109, 113] .
		

Links

• Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened

Crossrefs

Cf. A182134 (row lengths), A245722 (row products), A245396, A249669, A010051, A000040.

Programs

Haskell

a244365 n k = a244365_tabf !! (n-1) !! (k-1)
a244365_row n = a244365_tabf !! (n-1)
a244365_tabf = zipWith farideh (map (+ 1) a000040_list) a249669_list
               where farideh u v = filter ((== 1) .  a010051') [u..v]

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

Formula

T(n,k) = A000040(n+k) for k = 1 .. A182134(n).