A275681 Table read by rows: list of sexy prime triples (p, p+6, p+12) such that p+18 is composite.

7, 13, 19, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 73, 79, 97, 103, 109, 101, 107, 113, 151, 157, 163, 167, 173, 179, 227, 233, 239, 257, 263, 269, 271, 277, 283, 347, 353, 359, 367, 373, 379, 557, 563, 569, 587, 593, 599, 607, 613, 619, 647, 653, 659, 727, 733, 739

Offset: 1

Author

Arkadiusz Wesolowski, Aug 05 2016

Keywords

• nonn
• tabf

Examples

			The table starts:
7, 13, 19;
17, 23, 29;
31, 37, 43;
...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Wikipedia, Sexy prime
• Index entries for primes, gaps between

Crossrefs

Cf. A023201 (sexy primes), A046118, A123082, A275682.

Programs

Magma

lst:=[]; for p in PrimesUpTo(727) do b:=p+6; if IsPrime(b) then c:=b+6; if IsPrime(c) and not IsPrime(c+6) then lst:=lst cat [p, b, c]; end if; end if; end for; lst;

Maple

N:= 10^4: # to get all entries <= N
Primes:= select(isprime,{seq(i,i=1..N+18,2)}):
S:= select(`<=`, Primes,N) intersect map(t -> t-6, Primes) intersect map(t -> t-12, Primes) minus map(t -> t-18, Primes):
map(t ->(t,t+6,t+12), sort(convert(S,list))); # Robert Israel, Aug 05 2016

Mathematica

Most[#]&/@Select[Table[n+{0,6,12,18},{n,Prime[Range[200]]}],PrimeQ[#] == {True,True,True,False}&]//Flatten (* Harvey P. Dale, Jan 19 2017 *)

Formula

a(3*n-2) = A046118(n).

a(3*n-1) = A046118(n)+6.

a(3*n) = A046118(n)+12.