A090303 Begin with n and consider numbers obtained by successively subtracting 2,3,5,7,11,...; a(n) = largest prime that arises, i.e., largest prime of the form n - sum prime(r), or 0 if no such prime exists.

0, 0, 0, 2, 3, 0, 5, 3, 7, 5, 0, 7, 11, 0, 13, 11, 7, 13, 17, 3, 19, 17, 13, 19, 23, 0, 17, 23, 19, 13, 29, 0, 31, 29, 7, 31, 0, 0, 37, 23, 31, 37, 41, 3, 43, 41, 37, 43, 47, 0, 41, 47, 43, 37, 53, 0, 47, 53, 31, 43, 59, 0, 61, 59, 37, 61, 0, 0, 67, 53, 61, 67, 71, 0, 73, 71, 67, 73, 2, 3

Offset

1,4

Comments

a(p) = p-2 if p is larger member of a twin prime pair.

Conjecture: There are finitely many zeros in this sequence.

Links

Table of n, a(n) for n=1..80.

Formula

Largest prime of the form n - sum prime(r).

Prog

(PARI) a(n) = {p = 2; n -= p; while ((n > 0) && !isprime(n), p = nextprime(p+1); n -= p); max(0, n); } \\ Michel Marcus, Jul 29 2017

Crossrefs

Cf. A090304.

Sequence in context: A080367 A354365 A066913 * A277516 A322333 A346615

Adjacent sequences: A090300 A090301 A090302 * A090304 A090305 A090306

Keyword

nonn

Author

Amarnath Murthy, Nov 30 2003

Extensions

More terms from David Wasserman, Oct 27 2005

Status

approved