|
|
A190414
|
|
primepi(R_m) <= i*primepi(R_j) for any factorization m=i*j if j >= a(i), where R_k is the k-th Ramanujan prime (A104272).
|
|
2
|
|
|
1, 2490, 567, 756, 425, 510, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This is another interpretation of Conjecture 1 in the paper by Sondow, Nicholson, and Noe. The conjecture has been verified for i <= 20 and Ramanujan primes less than 10^9.
The conjecture has been proven for i > 38 and j > 9 by Christian Axler. Complete exception list can be found in remark of paper. - John W. Nicholson, Aug 04 2019
|
|
LINKS
|
|
|
FORMULA
|
For all n >= 20, a(n) = 2*n.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|