login
A244365
Table read by rows: row n contains all primes p such that prime(n) < p <= floor(prime(n)^(1+1/n)).
5
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
1,1
COMMENTS
Length of n-th row = A182134(n);
T(n,1) = A000040(n+1); T(n,A182134(n)) = A245396(n).
LINKS
FORMULA
T(n,k) = A000040(n+k) for k = 1 .. A182134(n).
EXAMPLE
. 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] .
PROG
(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
CROSSREFS
Cf. A182134 (row lengths), A245722 (row products), A245396, A249669, A010051, A000040.
Sequence in context: A355918 A003255 A263321 * A171014 A254050 A250094
KEYWORD
nonn,tabf
AUTHOR
Reinhard Zumkeller, Nov 16 2014
STATUS
approved