A221309 Numbers m such that no subset of {m-1, m, m+1} sums up to a prime number.

25, 77, 85, 92, 93, 94, 118, 122, 123, 124, 133, 143, 144, 145, 160, 161, 170, 171, 185, 188, 202, 203, 206, 207, 208, 213, 214, 218, 235, 236, 237, 247, 248, 253, 259, 265, 266, 267, 275, 287, 290, 291, 295, 298, 302, 305, 319, 325, 328, 333, 334, 335, 340

Offset: 1

Author

Reinhard Zumkeller, Jan 10 2013

Keywords

• nonn

Comments

A117499(a(n)) = 0.

Examples

			a(1) = 25: there are 7 nonempty subsets of {25-1, 25, 25+1}: {24}, {25}, {26}, {24,25}, {24,26}, {25,26} and {24,25,26} with sums and factorizations: 24=3*2^3, 25=5^2, 26=13*2, 49=7^2, 50=5^2*2, 51=17*3 and 75=5^2*3.
		

Links

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

Crossrefs

Subsequence of A079364.

Programs

Haskell

a221309 n = a221309_list !! (n-1)
a221309_list = map (+ 1) $ elemIndices 0 a117499_list

Mathematica

Flatten@Position[
  Plus @@ # & /@ (Rest@Subsets[# + {-1, 0, 1}]) & /@
Range@340, {?(! PrimeQ@# &) ..}] (* _Hans Rudolf Widmer, Oct 26 2024 *)