OFFSET
1,2
COMMENTS
Sequence is infinite since the primes have density 0. - Charles R Greathouse IV, Apr 28 2011
EXAMPLE
5 is a term of the series, as 5+1, 5+3 and 5+3+1 are all nonprime. The next term, 87, is the next number k such that k+1, k+3, k+1+3, k+5, k+1+5, k+3+5 and k+1+3+5 are all nonprime.
MATHEMATICA
(* first do *) Needs["Combinatorica`"] (* then *) lst = {}; g[k_] := Block[{j = 1, l = 2^Length@lst}, While[j < l && !PrimeQ[Plus @@ NthSubset[j, lst] + k], j++ ]; If[j == l, False, True]]; f[n_] := Block[{k = lst[[ -1]] + 1}, While[g[k] == True, k++ ]; AppendTo[lst, k]; k]; Do[Print@f@n, {n, 10}]; (* Robert G. Wilson v, Dec 31 2007 *)
(* Second program, avoids "Combinatorica`": *)
Nest[Append[#, Block[{k = Last@ # + 1}, While[AnyTrue[Total /@ Select[Subsets[Append[#, k]], Length@ # > 1 &], PrimeQ], k++ ]; k ] ] &, {1}, 6] (* Michael De Vlieger, Jun 11 2018 *)
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Randy L. Ekl, Dec 28 2007
EXTENSIONS
a(9) from Robert G. Wilson v, Dec 31 2007
a(10) from Donovan Johnson, Feb 15 2008
STATUS
approved