OFFSET
1,1
COMMENTS
Conjecture: Except for first term, the sequence coincides with A001359. This is true for all primes < 2*10^7.
Conjecture: Except for first term, the sequence coincides with A001359. This is true for all primes < 7*10^16. Let n >= 2 be an integer, N +- 1 and M +- 1 two consecutive twin pairs where M>n*N. Finding a counterexample is the same as finding two consecutive primes P1 and P2 with n*N<P1<M and P2-P1 <= n. However, such gaps are unknown even for n=2.
The smallest prime(n) such that prime(n+1)/prime(n) is decreasing. [Thomas Ordowski, May 13 2012]
This sequence corresponds with A001359 for all terms less than 10^100. - Charles R Greathouse IV, May 14 2012
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
a(0)=2 and the record is 2/(3-2)=2; a(1)<>3 because 3/(5-3)=1.5; a(1)=5 because 5/(7-5)=2.5
MATHEMATICA
rmax = 0; p = 2; seq = {}; Do[q = NextPrime[p]; r = p/(q-p); If[r > rmax, rmax = r; AppendTo[seq, p]]; p = q, {100}]; seq (* Amiram Eldar, Dec 24 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Bernardo Boncompagni, Oct 21 2005
STATUS
approved