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%I #10 Jan 28 2017 21:36:59
%S 5011,7001,11251,22501,32303,32411,90031,101107,104123,108011,111323,
%T 121343,122131,124001,125101,141023,224011,233021,235003,241141,
%U 321203,324011,421303,432031,442201,510331,511213,520411,801011,1000183,1000541,1001191,1005223,1006231
%N Primes p whose binary representation p_2 is the decimal representation of a prime q; and also the sum of the decimal digits of p equals the sum of the digits of p_2.
%C Intersection of A037308 and A065720.
%e a(1) = 5011 is a prime;
%e 5011_2 = 1001110010011_10 is a prime;
%e 5 + 0 + 1 + 1 = 7;
%e 1 + 0 + 0 + 1 + 1 + 1 + 0 + 0 + 1 + 0 + 0 + 1 + 1 = 7; both the digit sums are equal.
%t Select[Prime[Range[1000000]], PrimeQ[FromDigits[IntegerDigits[#, 2]]] && Plus @@ IntegerDigits[#] == Plus @@ IntegerDigits[FromDigits[IntegerDigits[#, 2]]] &]
%o (PARI) eva(n) = subst(Pol(n), x, 10)
%o is(n) = ispseudoprime(n) && ispseudoprime(eva(binary(n))) && sumdigits(n)==sumdigits(eva(binary(n))) \\ _Felix Fröhlich_, Jan 19 2017
%Y Cf. A000040, A033548, A037308, A065720, A089971.
%K nonn,base
%O 1,1
%A _K. D. Bajpai_, Jan 19 2017