A129823 Four consecutive nonprime odd numbers {n-1,n+1,n+3,n+5}.

115, 117, 119, 121, 117, 119, 121, 123, 119, 121, 123, 125, 141, 143, 145, 147, 183, 185, 187, 189, 201, 203, 205, 207, 203, 205, 207, 209, 213, 215, 217, 219, 215, 217, 219, 221, 243, 245, 247, 249, 285, 287, 289, 291, 295, 297, 299, 301, 297, 299, 301

Offset

1,1

Comments

These quartets seem to correspond to larger Prime gaps: the larger the primes gaps the more runs of odd nonprimes.

Links

Table of n, a(n) for n=1..51.

Formula

a(n) = {n-1,n+1,n+3,n+5} for both odd and both nonprime.

Mathematica

Flatten[Table[If[OddQ[n - 1] && PrimeQ[n - 1] == False && PrimeQ[n + 1] == False && PrimeQ[n + 3] == False && PrimeQ[n + 5] == False, {{n - 1}, {n + 1}, {n + 3}, (n + 5)}, {}], {n, 2, 300}]]
Select[Partition[Range[1, 311, 2], 4, 1], NoneTrue[#, PrimeQ]&]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 21 2016 *)

Crossrefs

Sequence in context: A084877 A060309 A101111 * A056035 A105993 A036269

Adjacent sequences: A129820 A129821 A129822 * A129824 A129825 A129826

Keyword

nonn,uned

Author

Roger L. Bagula, May 20 2007

Status

approved