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%I #31 Jan 02 2023 12:30:47
%S 171,3801,5781,8721,8781,17601,18231,19011,24741,28251,40431,48951,
%T 49371,58821,70521,79401,79701,83391,87321,95781,96501,99501,102861,
%U 109431,123171,125061,137091,177201,220311,224511,225561,229551,242451
%N Numbers k with property that 19*k + {2,4,8,10} are two pairs of consecutive twin primes.
%C All terms == 6 (mod 15).
%C These are numbers n such that 19n+2 is in A007530. As proved by _Benoit Jubin_ and _Farideh Firoozbakht_ (SeqFan list, Dec 15 2008), they are == 21 (mod 30). The same holds for p=19 replaced by p=7,11,13,17,23,29,31,... with residue class n=27,9,3,27,3,21,9,... (mod 30). - _M. F. Hasler_, Dec 24 2008
%H Robert Israel, <a href="/A152926/b152926.txt">Table of n, a(n) for n = 1..10000</a>
%H Farideh Firoozbakht, <a href="http://list.seqfan.eu/oldermail/seqfan/2008-December/000342.html">all terms == 21 (mod 30)</a>, message on the SeqFan list, Dec 17 2008
%e 171 is in the sequence because 19*171 + {2,4} = {3251,3253} and 19*171 + {8,10} = {3257,3259} are 85th and 86th twin primes.
%e 3801 is in the sequence because 19*3801 + {2,4} = {72221,72223} and 19*3801 + {8,10} = {72227,72229} are 935th and 936th twin primes.
%p select(n -> andmap(t -> isprime(19*n+t), {2,4,8,10}), [seq(i,i=21..10^6,30)]); # _Robert Israel_, Mar 20 2018
%t Reap[For[n = 21, n < 10^6, n = n + 30, nn = 19*n + {2, 4, 8, 10}; If[CoprimeQ @@ nn, If[And @@ PrimeQ /@ nn, Sow[n]]]]][[2, 1]] (* _Jean-François Alcover_, Feb 25 2015 *)
%t Select[Range[6,243000,15],AllTrue[19#+{2,4,8,10},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 09 2020 *)
%Y Cf. A001359.
%Y Cf. A007530. - _M. F. Hasler_, Dec 24 2008
%K nonn
%O 1,1
%A _Zak Seidov_, Dec 15 2008
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