A117499 Number of subsets of {n-1, n, n+1} that sum up to a prime.

4, 4, 4, 3, 2, 4, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 0, 1, 1, 1, 2, 4, 2, 1, 1, 1, 1, 3, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 0, 2, 2, 1, 1, 2, 2, 2, 0, 1, 1, 1, 2, 3, 1, 0, 0, 0, 1, 3, 2, 2, 2, 2, 1, 2, 1, 1, 1

Offset: 1

Author

Reinhard Zumkeller, Mar 23 2006

Keywords

• nonn

Comments

0 <= a(n) <= 4; a(A066388(n)) = 4.

a(A221309(n)) = 0; a(A221310(n)) = 4. - Reinhard Zumkeller, Jan 10 2013

Examples

			a(1) = #{2, 0+2=2, 1+2=3, 0+1+2=3} = 4;
a(2) = #{2, 3, 1+2=3, 2+3=5} = 4;
a(3) = #{2, 3, 2+3=5, 3+4=7} = 4;
a(4) = #{3, 5, 3+4=7} = 3;
a(5) = #{5, 5+6=11} = 2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010051.

Programs

Haskell

a117499 1 = sum $ map a010051 [1, 2, 0 + 1, 0 + 2, 1 + 2, 0 + 1 + 2]
a117499 n = sum $ map a010051 [n - 1, n, n + 1, 2 * n - 1, 2 * n + 1]
-- Reinhard Zumkeller, Jan 10 2013

Mathematica

Table[Length[Select[{-1+n,n,1+n,-1+2 n,2 n,1+2 n,3 n},PrimeQ]],{n,105}]
ssp[{a_,b_,c_}]:=Count[Subsets[{a,b,c},3],?(PrimeQ[Total[#]]&)]; ssp/@ Partition[ Range[0,110],3,1] (* _Harvey P. Dale, Jan 29 2013 *)

Formula

a(n) = A010051(n-1) + A010051(n) + A010051(n+1) + A010051(2*n-1) + A010051(2*n) + A010051(2*n+1).