cp's OEIS Frontend

A256872 Numbers whose binary expansion is the concatenation of the binary expansion of two prime numbers in at least two ways.

%I A256872 #8 Apr 21 2015 22:49:29
%S A256872 23,31,45,47,61,93,95,119,125,127,175,187,189,191,239,247,253,255,335,
%T A256872 357,359,363,369,379,381,383,431,439,455,477,485,491,493,495,507,509,
%U A256872 511,573,575,631,637,639,669,671
%N A256872 Numbers whose binary expansion is the concatenation of the binary expansion of two prime numbers in at least two ways.
%C A256872 A simplified variant (and subsequence) of A257318 (and A090421) where the concatenation of any number of primes is considered.
%C A256872 The subsequence of numbers which are concatenation of 2 primes in at least 3 ways is (93, 95, 189, 191, 239, 253, 335, 381, 383, 669, ...).
%C A256872 All terms are odd. Indeed, if an even number n > 2 is concatenation of two primes (in binary), then it is of the form 'n' = 'floor(n/4)''2' (where 'x' is x in binary), and there is no other possible decomposition.
%F A256872 A090418(a(n)) >= 2. (Necessary but not sufficient condition. This actually characterizes elements of A257318. For example, all terms of A090423 satisfy this but many of them are not terms of this sequence.)
%e A256872 23 = 10111[2] = (10[2])(111[2]) = (101[2])(11[2]) which is (2)(7) resp. (5)(3).
%o A256872 (PARI) is(n,c=2)={for(i=2,#binary(n)-2,bittest(n,i-1)&&isprime(n>>i)&&isprime(n%2^i)&&!c--&&return(1))}
%Y A256872 Cf. A090418, A090421, A090423, A257318.
%K A256872 nonn,base
%O A256872 1,1
%A A256872 _M. F. Hasler_, Apr 21 2015