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.

5011, 7001, 11251, 22501, 32303, 32411, 90031, 101107, 104123, 108011, 111323, 121343, 122131, 124001, 125101, 141023, 224011, 233021, 235003, 241141, 321203, 324011, 421303, 432031, 442201, 510331, 511213, 520411, 801011, 1000183, 1000541, 1001191, 1005223, 1006231

Offset: 1

Author

K. D. Bajpai, Jan 19 2017

Keywords

• nonn
• base

Comments

Intersection of A037308 and A065720.

Examples

			a(1) = 5011 is a prime;
5011_2 = 1001110010011_10 is a prime;
5 + 0 + 1 + 1 = 7;
1 + 0 + 0 + 1 + 1 + 1 + 0 + 0 + 1 + 0 + 0 + 1 + 1 = 7; both the digit sums are equal.
		

Crossrefs

Cf. A000040, A033548, A037308, A065720, A089971.

Programs

Mathematica

Select[Prime[Range[1000000]], PrimeQ[FromDigits[IntegerDigits[#, 2]]] && Plus @@ IntegerDigits[#] == Plus @@ IntegerDigits[FromDigits[IntegerDigits[#, 2]]] &]

PARI

eva(n) = subst(Pol(n), x, 10)
is(n) = ispseudoprime(n) && ispseudoprime(eva(binary(n))) && sumdigits(n)==sumdigits(eva(binary(n))) \\ Felix Fröhlich, Jan 19 2017