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A281299 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. 0

%I

%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

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Last modified November 29 02:45 EST 2020. Contains 338756 sequences. (Running on oeis4.)