|
|
A215237
|
|
Least number k for which primepi(prime(k+1)/2) - primepi(prime(k)/2) = n.
|
|
3
|
|
|
1, 2, 30, 259, 429, 4612, 26466, 88110, 31545, 104071, 2775456, 14614604, 15793779, 164082567, 476853784, 495207013, 3613011290, 9032608100, 69827848342
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Equivalently stated, a(n) is least k such that there are exactly n primes between prime(k)/2 and prime(k+1)/2. - Peter Munn, May 20 2019
|
|
LINKS
|
|
|
EXAMPLE
|
For n = 2, the consecutive primes are 113 and 127; there are two primes between 56.5 and 63.5. For n = 3, the consecutive primes are 1637 and 1657; there are three primes between 818.5 and 828.5.
|
|
MATHEMATICA
|
t = Table[PrimePi[Prime[n+1]/2] - PrimePi[Prime[n]/2], {n, 100000}]; Flatten[Table[Position[t, n, 1, 1], {n, 0, 8}]]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more,hard
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|