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A278923 Largest p such that 2n-1 = p + q + r with three primes p < q < r, or 0 if no such primes exist. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A261922 A078907 A282135 * A210485 A111815 A281269

Adjacent sequences:  A278920 A278921 A278922 * A278924 A278925 A278926

KEYWORD

nonn

AUTHOR

M. F. Hasler, Dec 01 2016

STATUS

approved

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Last modified October 17 13:27 EDT 2018. Contains 316280 sequences. (Running on oeis4.)