OFFSET
0,5
COMMENTS
All terms conjecturally are found. Note that according to the definition a(k,0) is the k-th term of the sequence {p | p is prime} namely for every positive integer k, a(k,0) = prime(k). Hence if Firoozbakht's conjecture is true then a(0)=1.
LINKS
EXAMPLE
a(0)=a(1)=a(2)=a(3)=1 conjecturally states that the four sequences A000040, A001359, A023200 and A023201 have this property: For every positive integer n, b(n) exists and b(n+1) < b(n)^(1+1/n). Namely b(n)^(1/n) is a strictly decreasing function of n.
If in the definition instead of the sequence {p | p and p+2n are primes} we set {p | p is prime and nextprime(p)=p+2n} then it seems that except for n=3 all terms of the new sequence {c(n)} are equal to 1 and for n=3, c(3)=7746. Note that c(3)=7746 means that the sequence {p | p is prime and nextprime(p)=p+6} = A031924 has this property: For all k >= 7746, A031924(k+1)^(1/(k+1)) < A031924(k)^(1/k).
CROSSREFS
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht and Jahangeer Kholdi, Nov 25 2014
STATUS
approved