A280708 Lexicographically earliest sequence such that no subsequence sums to a prime.

1, 8, 24, 24, 86, 1260, 1890, 14136, 197400, 10467660, 1231572090

Offset: 1

Author

Peter Kagey, Jan 07 2017

Keywords

• nonn
• hard
• more

Comments

This sequence is monotonically increasing.

So far, apart from a(4) this sequence is identical to A052349.

Examples

			For n = 4, a(4) = 24 because all subsets have nonprime sums:
           1 +  8 =  9 = 3^2
           1 + 24 = 25 = 5^2
           8 + 24 = 32 = 2^5
          24 + 24 = 48 = 2^4*3
      1 +  8 + 24 = 33 = 3*11
      1 + 24 + 24 = 49 = 7^2
      8 + 24 + 24 = 56 = 2^3*7
  1 + 8 + 24 + 24 = 57 = 3*19
		

Crossrefs

Cf. A052349.

Programs

Maple

S:= {0}: count:= 0:
x:= 1:
while x < 10^6 do
  if ormap(s -> isprime(s+x), S) then x:= x+1
  else
    count:= count+1;
    A[count]:= x;
    S:= S union map(`+`,S,x);
  fi
od:
seq(A[i],i=1..count); # Robert Israel, Jan 20 2017

Mathematica

t = {1}; c = 1; Print[1]; While[Length[t] < 11, r = Rest[Subsets[t]]; s = Table[Total[r[[i]]], {i, Length[r]}]; While[PrimeQ[c] || Union[PrimeQ[s + c]] != {False}, c++]; Print[c]; AppendTo[t, c]] (* Hans Havermann, Jan 20 2017 *)

Extensions

a(9) and a(10) from Dmitry Kamenetsky, Jan 12 2017

a(11) from Hans Havermann, Jan 20 2017