|
| |
|
|
A092940
|
|
a(n) = largest prime p such that 2*prime(n) - p is prime.
|
|
3
| |
|
|
2, 3, 7, 11, 19, 23, 31, 31, 43, 53, 59, 71, 79, 83, 89, 103, 113, 109, 131, 139, 139, 151, 163, 173, 191, 199, 199, 211, 211, 223, 251, 257, 271, 271, 293, 283, 311, 313, 331, 317, 353, 359, 379, 383, 389, 379, 419, 443, 449, 439, 463, 467, 479, 499, 509, 523
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| a(n) = largest prime p such that prime(n) = (p+q)/2, where q is also prime.
prime(n) <= a(n) < 2*prime(n).
Conjecture: a(n) = prime(n) only for n = 1 and 2.
|
|
|
FORMULA
| a(n) = 2*prime(n) - A092938(n).
|
|
|
EXAMPLE
| 2*prime(18) = 122; the primes smaller than 122 are 113, 109, 107, ... in descending order. 122 - 113 = 9 is not prime, but 122 - 109 = 13 is prime, hence a(18) = 109.
|
|
|
PROG
| (PARI) {for(n=1, 56, k=2*prime(n); q=2; while(!isprime(p=k-q), q=nextprime(q+1)); print1(p, ", "))} - Klaus Brockhaus, Dec 23 2006
|
|
|
CROSSREFS
| Cf. A092938, A092939, A116619.
Sequence in context: A140409 A108541 A038937 * A045326 A195602 A105897
Adjacent sequences: A092937 A092938 A092939 * A092941 A092942 A092943
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 23 2004
|
|
|
EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 23 2006
|
| |
|
|
