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A282324 Greater of twin primes congruent to 19 (mod 30).

%I A282324 #34 Sep 08 2022 08:46:18
%S A282324 19,109,139,199,229,349,619,829,859,1279,1429,1489,1609,1669,1699,
%T A282324 1789,1879,1999,2029,2089,2239,2269,2659,2689,3169,3259,3469,3529,
%U A282324 3559,3769,3919,4129,4159,4219,4339,4519,4549,4639,4789,4969,5419,5479,5659,5869,6199
%N A282324 Greater of twin primes congruent to 19 (mod 30).
%C A282324 The union of [A282323 and this sequence] is A132242.
%C A282324 The union of [{5, 7}, A282322, this sequence and A282326] is the greater of twin primes sequence A006512.
%C A282324 The union of [{3, 5, 7}, A282321 to A282326] is the twin primes sequence A001097.
%C A282324 Number of terms less than 10^k, k=2,3,4,...: 1, 9, 64, 414, 2734, 19674, 146953, ... - _Muniru A Asiru_, Feb 09 2018
%H A282324 Muniru A Asiru, <a href="/A282324/b282324.txt">Table of n, a(n) for n = 1..2000</a>
%p A282324 a:={}:
%p A282324 for i from 1 to 1229 do
%p A282324   if isprime(ithprime(i)-2) and ithprime(i) mod 30 = 19 then
%p A282324     a:={op(a),ithprime(i)}:
%p A282324   fi:
%p A282324 od:
%p A282324 a;
%p A282324 # More efficient
%p A282324 select(n -> isprime(n-2) and isprime(n), [seq(30*k+19, k=0..220)]); # _Muniru A Asiru_, Jan 30 2018
%t A282324 Select[Prime[Range[1000]], PrimeQ[# - 2] && Mod[#, 30] == 19 &] (* _Vincenzo Librandi_, Feb 13 2017 *)
%o A282324 (Magma) [p: p in PrimesUpTo(7000) | IsPrime(p-2) and p mod 30 eq 19 ]; // _Vincenzo Librandi_, Feb 13 2017
%o A282324 (PARI) list(lim)=my(v=List(), p=2); forprime(q=3, lim, if(q-p==2 && q%30==19, listput(v, q)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Feb 14 2017
%o A282324 (GAP) Filtered(List([1..220], k -> 30*k-11), n -> IsPrime(n) and IsPrime(n-2));  # _Muniru A Asiru_, Feb 02 2018
%Y A282324 Subset of A001097, A006512, A132234, A132242 and A132247.
%Y A282324 Cf. A001359, A132235, A132236, A232880, A232881, A232882, A282321, A282322, A282323, A060229, A282326.
%K A282324 nonn
%O A282324 1,1
%A A282324 _Martin Renner_, Feb 11 2017