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

1,1

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, ...

Links

Table of n, a(n) for n=1..17.

Formula

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

Example

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

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

Crossrefs

Cf. A115760.

Sequence in context: A294774 A192746 A081295 * A233187 A160426 A301786

Adjacent sequences: A180562 A180563 A180564 * A180566 A180567 A180568

Keyword

nonn,more

Author

Michel Lagneau, Jan 21 2011

Extensions

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

Status

approved