A278922 -id:A278922 - cp's OEIS frontend

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

M. F. Hasler, Dec 01 2016

nonn

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).

David W. Wilson, Table of n, a(n) for n = 1..10000
Index entries for sequences related to Goldbach conjecture

Cf. A278922.

Cf. A278373, complement of A056996.

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)))

cp's OEIS Frontend

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

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