A180565 Numbers starting with 5 such that the sum of any two distinct entries is two times some prime.

5, 9, 17, 29, 77, 197, 689, 44537, 159617, 374249, 695957, 4343237, 8439595349, 196119836669, 45036059849537, 108841069412237, 505069584287297

Offset: 1

Author

Michel Lagneau, Jan 21 2011

Keywords

• nonn
• more

Comments

The numbers starting with 1 are in the set {1, 5, 9} because if another number q = 2k + 1 exists, then k+1, k+3 and k+5 are primes only if k = 2, but q=5 is already in the set.

The numbers starting with 3 are given by A115760.

The numbers starting with 7 are 7, 15, 19, 67, 127, 187, 547, 607, ...

Examples

			For the set of the first three entries, 5+9 = 2*7, 5+17 = 2*11, 9+17 = 2*13.
		

Crossrefs

Cf. A115760.

Programs

Maple

A180565 := proc(n) option remember; if n = 1 then 5; else for a from procname(n-1)+1 do wrks := true ; for prev from 1 to n-1 do if not type((procname(prev)+a)/2,prime) then wrks := false; break; end if; end do: if wrks then return a; end if; end do: end if; end proc: # R. J. Mathar, Jan 24 2011

Formula

a(n) = 2*A093483(n)+1 (follows from the definition). - Chris Boyd, Mar 16 2014

Extensions

a(14)-a(17) from Chris Boyd, Mar 16 2014