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A181603 Twin primes ending in 1.

%I A181603 #14 Oct 24 2021 11:27:56
%S A181603 11,31,41,61,71,101,151,181,191,241,271,281,311,421,431,461,521,571,
%T A181603 601,641,661,811,821,881,1021,1031,1051,1061,1091,1151,1231,1291,1301,
%U A181603 1321,1451,1481,1621,1721,1871,1931,1951,2081,2111,2131,2141,2311,2341,2381
%N A181603 Twin primes ending in 1.
%C A181603 These are twin primes == 1 (mod 30) or == 11 (mod 30) or == 21 (mod 30). In the first case they cannot be lower twin primes because the upper ones would be == 3 (mod 30) and divisible by 3. In the second case they cannot be upper twin primes because the lower ones would be == 9 (mod 30) and divisible by 3. The last case is excluded because that implies they are divisible by 3. In summary the upper twin primes in here are given by A282326, the lower twin primes in here by A282321. - _R. J. Mathar_, Feb 14 2017
%H A181603 Harvey P. Dale, <a href="/A181603/b181603.txt">Table of n, a(n) for n = 1..1000</a>
%H A181603 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>
%p A181603 isA181603 := proc(p)
%p A181603     if isprime(p) and (isprime(p-2) or isprime(p+2)) then
%p A181603         if modp(p,10) = 1 then
%p A181603             true;
%p A181603         else
%p A181603             false;
%p A181603         end if ;
%p A181603     else
%p A181603         false;
%p A181603     end if;
%p A181603 end proc:
%p A181603 for n from 1 to 1000 do
%p A181603     if isA181603(n) then
%p A181603         printf("%d,",n) ;
%p A181603     end if;
%p A181603 end do: # _R. J. Mathar_, Feb 14 2017
%t A181603 Select[Prime@ Range@ 360, Mod[ #, 10] == 1 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* _Robert G. Wilson v_, Nov 06 2010 *)
%t A181603 Select[Flatten[Select[Partition[Prime[Range[400]],2,1],#[[2]]-#[[1]] == 2&]],Mod[#,10]==1&] (* _Harvey P. Dale_, Oct 24 2021 *)
%Y A181603 Cf. A001097, A181604, A181605, A181606.
%K A181603 base,nonn
%O A181603 1,1
%A A181603 _Omar E. Pol_, Nov 01 2010
%E A181603 More terms from _Robert G. Wilson v_, Nov 06 2010