A229992 Numbers for which A061214(n) + 1 is prime, where A061214(n) = product of composite numbers between prime(n) and prime(n+1) .

2, 3, 5, 6, 7, 8, 10, 12, 13, 14, 16, 17, 20, 21, 25, 26, 28, 29, 31, 33, 35, 39, 41, 43, 44, 45, 49, 51, 52, 57, 60, 64, 67, 69, 70, 81, 83, 85, 89, 90, 91, 97, 98, 104, 109, 113, 116, 118, 120, 131, 134, 136, 140, 142, 144, 145, 148, 152, 157, 171, 173

Offset

2,1

Links

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

Example

a(2) = 2 because 4 + 1 is prime; a(3) = 3 because 6 + 1 is prime; 4 is not in A229992 because 8*9*10 + 1 is not prime.

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 = Rest[Flatten[Position[t, 1]]]
Rest[Flatten[Position[Times@@@(Range[#[[1]]+1, #[[2]]-1]&/@Partition[Prime[Range[200]], 2, 1])+1, _?PrimeQ]]] (* Harvey P. Dale, Feb 18 2026 *)

Crossrefs

Cf. A061214, A229992.

Sequence in context: A329898 A145353 A013936 * A076437 A028790 A028748

Adjacent sequences: A229989 A229990 A229991 * A229993 A229994 A229995

Keyword

nonn

Author

Clark Kimberling, Oct 09 2013

Status

approved