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A133660
No sum of 2 or more terms equals a prime.
6
1, 3, 5, 87, 113, 1151, 5371, 199276, 32281747, 16946784207
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
Sequence in context: A182234 A308612 A082715 * A271925 A236365 A057663
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