OFFSET
1,1
COMMENTS
A prime 5-tuple is a constellation of five successive primes with distance 12, and is of the form (p, p+2, p+6, p+8, p+12) or (p, p+4, p+6, p+10, p+12).
Initial members p (other than 7) of prime 5-tuples of the form (p, p+4, p+6, p+10, p+12) are congruent to 97 or 187 (mod 210).
Also called prime 5-tuples of the second kind.
LINKS
Robert Israel, Table of n, a(n) for n = 1..5665
C. K. Caldwell, Top Twenty page, Quintuplet
Eric Weisstein's World of Mathematics, Prime Constellation
Wikipedia, Prime quadruplet
FORMULA
a(5*n-4) = A022007(n).
MAPLE
Primes:= select(isprime, [seq(i, i=3..10^5, 2)]):
T:= select(t -> Primes[t+4]-Primes[t]=12 and Primes[t+1]-Primes[t]=4, [$1..nops(Primes)-5]):
seq(seq(Primes[t+j], j=0..4), t=T); # Robert Israel, Jul 13 2016
MATHEMATICA
m = {0, 4, 6, 10, 12}; Union@ Flatten@ Map[# + m &, Select[Prime@ Range[10^4], Times @@ Boole@ PrimeQ[# + m] == 1 &]] (* Michael De Vlieger, Jul 13 2016 *)
PROG
(Magma) lst:=[]; for p in [5..43777 by 2] do if p le 7 xor p mod 210 in {97, 187} then if IsPrime(p) then t:=[c: c in [p+4..p+12] | IsPrime(c)]; if #t eq 4 then lst:=lst cat [p] cat t; end if; end if; end if; end for; lst;
(MATLAB)
Primes = primes(2*10^8);
T12 = find(Primes(5:end) - Primes(1:end-4)==12);
T4 = find(Primes(2:end) - Primes(1:end-1)==4);
T = intersect(T4, T12);
Primes(reshape([T; T+1; T+2; T+3; T+4], 5*numel(T), 1)) % Robert Israel, Jul 14 2016
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Arkadiusz Wesolowski, Jul 12 2016
STATUS
approved