A133660 No sum of 2 or more terms equals a prime.

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

Links

Table of n, a(n) for n=1..10.

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

Cf. A052349, A133661.

Sequence in context: A182234 A308612 A082715 * A271925 A236365 A057663

Adjacent sequences: A133657 A133658 A133659 * A133661 A133662 A133663

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