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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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,more
AUTHOR
Michel Lagneau, Jan 21 2011
EXTENSIONS
a(14)-a(17) from Chris Boyd, Mar 16 2014
STATUS
approved

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Last modified February 21 04:08 EST 2024. Contains 370219 sequences. (Running on oeis4.)