A229991 Numbers for which A061214(n) - 1 is prime, where A061214(n) = product of composite numbers between prime(n) and prime(n+1) .

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 17, 19, 20, 22, 26, 28, 29, 33, 34, 35, 41, 43, 45, 49, 52, 55, 56, 57, 60, 61, 64, 69, 72, 75, 81, 83, 85, 86, 89, 90, 91, 93, 94, 98, 104, 105, 109, 113, 116, 120, 122, 123, 124, 129, 134, 138, 139, 140, 142, 143

Offset: 2

Author

Clark Kimberling, Oct 09 2013

Keywords

• nonn

Examples

			a(2) = 2 because 4 - 1 is prime; a(4) = 4 because 8*9*10-1 is prime; 12 is not in A229991 because 38*39*40 - 1 is not prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A061214, A229992.

Programs

Mathematica

q[n_] := Product[k, {k, Prime[n] + 1, Prime[n + 1] - 1}]; c[n_] := If[PrimeQ[q[n] - 1], 1, 0]; t = Table[c[n], {n, 1, 230}]; u = Flatten[Position[t, 1]]
Select[Range[150],PrimeQ[Times@@Range[Prime[#]+1,Prime[#+1]-1]-1]&] (* Harvey P. Dale, Feb 15 2014 *)