A127523 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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, 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

Table of n, a(n) for n=1..105.

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

Sequence in context: A280800 A083889 A360079 * A364389 A116927 A137276

Adjacent sequences: A127520 A127521 A127522 * A127524 A127525 A127526

KEYWORD

nonn

AUTHOR

Zak Seidov, Apr 01 2007

STATUS

approved