This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A181493 #20 Aug 06 2025 22:36:18 %S A181493 6,12,192,786432 %N A181493 Numbers of the form 3*2^k which are the average of twin primes, i.e., a(n)-1 and a(n)+1 are both prime. %C A181493 Sequence A181490 lists the exponents k, sequences A181491 and A181492 the corresponding twin primes. %F A181493 A181493 = A014574 intersect A007283 = A181491 + 1 = A181492 - 1 = 3*2^A181490. %F A181493 A181493(n) = A007283(A181490(n)). %F A181493 A181493 = A014574 intersect A007283 = A181491 + 1 = A181492. %F A181493 A181493(n) = A007283(A181490(n)). %t A181493 Select[3 2^Range[500],PrimeQ[#-1]&&PrimeQ[#+1]&] (* _Harvey P. Dale_, Jan 18 2011 *) %o A181493 (PARI) for( k=1,999, ispseudoprime(3<<k-1)||next; ispseudoprime(3<<k+1)||next; print1(3<<k,", ")) %Y A181493 Cf. A001097, A001359, A006512, A014574. %K A181493 nonn,bref,more %O A181493 1,1 %A A181493 _M. F. Hasler_, Oct 30 2010