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%I #16 Jun 05 2017 11:43:25
%S 31,41,71,97,139,193,337,349,421,487,587,619,643,701,811,827,1021,
%T 1051,1093,1217,1249,1259,1471,1571,1721,1747,1861,1949,2087,2131,
%U 2383,2521,2549,2591,2957,3023,3083,3209,3529,3613,3779,3833,3947,4283,4409,4451,4481,4483,4567,4591,4733
%N Primes p such that 6p - 5 and 6p + 5 are consecutive primes.
%C a(n + 1) = a(n) + 2 for n = 47, 386, 868, 1000, 1247, 1521, 1834, 2271, 2435, 2437, 2468, 2483, 2811, 2819, 2960, 3202, 3531, 3581, 5021, 5178, 5245, 5669, 6009, 6087, 6198, 6686, 7017, 7029, 7454, 7576, 7699, 8557, 8940, 9018, 10130, 10240, 10449, 10578, 10952, 11070, 11103, 11199, ...
%C E.g., a(42)=4481 and a(43)=4483.
%H Robert Israel, <a href="/A284531/b284531.txt">Table of n, a(n) for n = 1..10000</a>
%e 31*6 - 5 = 181 = A000040(42) and 31*6 + 5 = 191 = A000040(43).
%p filter:= p -> isprime(p) and isprime(6*p-5) and isprime(6*p+5) and not isprime(6*p-1) and not isprime(6*p+1):
%p select(filter, [seq(i,i=3..10000, 2)]); # _Robert Israel_, Apr 07 2017
%t Select[Range[31,5000,2], PrimeQ[#] && PrimeQ[a = 6 # - 5] && NextPrime[a] == a + 10 &]
%t cp6Q[n_]:=Module[{p1=6n-5},PrimeQ[p1]&&NextPrime[p1]==6n+5]; Select[ Prime[ Range[ 1000]],cp6Q] (* _Harvey P. Dale_, Jun 05 2017 *)
%Y Subsequence of A127430. Cf. A000040.
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 28 2017
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