|
| |
|
|
A127523
|
|
a(n) = floor(p(n)*((log of p(n+2) to base p(n+1))-1)), where p(n) is n-th prime.
|
|
0
|
|
|
|
0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,29
|
|
|
COMMENTS
|
For the first 10000 terms: 1) values of terms are from 0..6. 2) numbers of occurrences of k = 0..6: {6010, 2959, 791, 197, 29, 13, 1} 3) positions of k=0..6 in the sequence: k=0: {1, 2, 4, 6, 9, 11, 12, 13, 16, 18, 19, 21, 24, ...}, k=1: {3, 5, 7, 8, 10, 14, 15, 17, 20, 22, 23, 31, 33, ...}, k=2: {29, 45, 46, 61, 65, 98, 136, 145, 149, 153, 161, 179, 204, ...}, k=3: {188, 262, 326, 366, 428, 445, 461, 589, 649, 684, 707, 731, 737, ..}, k=4: {216, 1830, 1878, 2190, 2343, 3076, 3426, 3731, 3794, 3860, 4008, 4563, 4753, ..}, k=5: {2224, 2809, 3643, 3792, 4230, 4259, 4521, 4611, 5948, 7809, 8359, 8687, 9833, ..}, k=6: {3384, ..}. Is the sequence bounded?
By Rankin's theorem the sequence is unbounded: in particular there are infinitely many n for which a(n) >> log log n log log log log n / (log log log n)^2. [Charles R Greathouse IV, Dec 20 2011]
|
|
|
LINKS
|
|
|
|
MATHEMATICA
|
a[n_]:=Floor[Prime[n]*(Log[Prime[n+1], Prime[n+2]]-1];
|
|
|
PROG
|
(PARI) p=2; q=3; forprime(r=5, 1e3, print1(p*log(r/q)\log(q)", "); p=q; q=r) \\ Charles R Greathouse IV, Dec 20 2011
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
