A278923 Largest p such that 2n-1 = p + q + r with three primes p < q < r, or 0 if no such primes exist.

0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 3, 5, 5, 3, 5, 7, 5, 7, 7, 7, 11, 11, 5, 11, 13, 11, 13, 13, 11, 17, 13, 13, 17, 17, 17, 19, 19, 13, 17, 19, 17, 23, 19, 19, 23, 23, 23, 23, 29, 23, 29, 29, 23, 29, 31, 31, 29, 31, 29, 31, 37, 29, 37, 37, 31, 41, 37, 31, 41, 37, 41, 43, 41, 41, 43, 43, 41, 43, 43, 47, 47, 43, 41, 47, 43, 47, 53, 47, 47, 53, 53, 53, 53, 59, 47

Offset

1,8

Comments

Empirically, such primes always exist for n >= 10, i.e., 2n-1 >= 19, whence a(n) >= 3 for all n >= 10. Again empirically, a(n) ~ 2n/3 as n -> oo and a(n) is always close to 2n/3.

This is the bisection (every other term) of A278922, whose terms with even indices are all equal to 2 (or 0).

Links

David W. Wilson, Table of n, a(n) for n = 1..10000

Index entries for sequences related to Goldbach conjecture

Prog

(PARI) a(n, p=(n=2*n-1)\3-1)=while(p=precprime(p-1), forprime(q=p+1, (n-p-1)\2, isprime(n-p-q)&&return(p)))

Crossrefs

Cf. A278922.

Cf. A278373, complement of A056996.

Sequence in context: A282135 A309339 A333453 * A210485 A111815 A281269

Adjacent sequences: A278920 A278921 A278922 * A278924 A278925 A278926

Keyword

nonn

Author

M. F. Hasler, Dec 01 2016

Status

approved