The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 FrÃ¶hlich_, Jan 19 2017

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

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jan 19 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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