

A180565


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


4



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



FORMULA



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(n1)+1 do wrks := true ; for prev from 1 to n1 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



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



