cp's OEIS Frontend

A282322 Greater of twin primes congruent to 13 (mod 30).

%I A282322 #41 Jan 19 2018 03:03:46
%S A282322 13,43,73,103,193,283,313,433,463,523,643,823,883,1033,1063,1093,1153,
%T A282322 1303,1453,1483,1723,1873,1933,2083,2113,2143,2383,2593,2713,2803,
%U A282322 3253,3373,3463,3583,3673,3823,3853,4003,4093,4243,4273,4423,4483,4723,4933,5023,5233,5443,5503,5653,5743
%N A282322 Greater of twin primes congruent to 13 (mod 30).
%C A282322 The union of [A282321 and this sequence] is A132241.
%C A282322 The union of [{5, 7}, this sequence, A282324 and A282326] is the greater of twin primes sequence A006512.
%C A282322 The union of [{3, 5, 7}, A282321 to A282326] is the twin primes sequence A001097.
%C A282322 A181604 without the 3. [Proof: working mod 10 we see that each value here is in A181604. For the other direction: Except 3 all twin primes in A181604 are upper twin primes; they cannot be lower twin primes because the upper ones would be multiples of 5. The twin primes in A181604 could be == 3 (mod 30) or == 13 (mod 30) or == 23 (mod 30). The first case is excluded because they would be multiples of 3; the third case is excluded because the lower twin primes would be == 21 (mod 30) and also multiples of 3. So only the case == 13 (mod 30) remains.] - _R. J. Mathar_, Feb 14 2017
%C A282322 Number of terms < 10^k for k >= 1: 0, 3, 13, 67, 401, 2736, 19797, 146841, 1141217, 9137078, ..., . - _Robert G. Wilson v_, Jan 07 2018
%H A282322 Muniru A Asiru, <a href="/A282322/b282322.txt">Table of n, a(n) for n = 1..20000</a>
%p A282322 a:={}:
%p A282322 for i from 1 to 1229 do
%p A282322   if isprime(ithprime(i)-2) and ithprime(i) mod 30 = 13 then
%p A282322     a:={op(a),ithprime(i)}:
%p A282322   fi:
%p A282322 od:
%p A282322 a;
%t A282322 Select[13 + 30 Range[0, 200], PrimeQ[# - 2] && PrimeQ[#] &] (* _Robert G. Wilson v_, Jan 07 2018 *)
%o A282322 (PARI) list(lim)=my(v=List(), p=2); forprime(q=3, lim, if(q-p==2 && q%30==13, listput(v, q)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Feb 14 2017
%Y A282322 Subset of A001097, A006512, A132233, A132241 and A132247.
%Y A282322 Cf. A001359, A232880, A232881, A232882, A282321, A282323, A282324, A282326.
%K A282322 nonn
%O A282322 1,1
%A A282322 _Martin Renner_, Feb 11 2017