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%I #34 Dec 27 2023 17:46:56
%S 3,5,7,11,13,17,19,31,37,41,47,59,61,67,73,79,97,103,107,109,127,131,
%T 137,151,157,167,173,179,181,191,193,199,211,223,227,229,233,239,241,
%U 251,257,271,283,307,313,331,367,379,397,409,419,421,431,433,439,443
%N Primes having in binary representation a prime number of 1's.
%C Same as primes with prime binary digit sum.
%C Primes with prime decimal digit sum are A046704.
%C Sum_{a(n) < x} 1/a(n) is asymptotic to log(log(log(x))) as x -> infinity; see Harman (2012). Thus the sequence is infinite. - _Jonathan Sondow_, Jun 09 2012
%C A049084(A000120(a(n))) > 0; A081091, A000215 and A081093 are subsequences.
%H Reinhard Zumkeller, <a href="/A081092/b081092.txt">Table of n, a(n) for n = 1..10000</a>
%H G. Harman, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Harman/harman2.html">Counting Primes whose Sum of Digits is Prime</a>, J. Integer Seq., 15 (2012), Article 12.2.2.
%e 15th prime = 47 = '101111' with five 1's, therefore 47 is in the sequence.
%p q:= n-> isprime(n) and isprime(add(i,i=Bits[Split](n))):
%p select(q, [$1..500])[]; # _Alois P. Heinz_, Sep 28 2023
%t Clear[BinSumOddQ];BinSumPrimeQ[a_]:=Module[{i,s=0},s=0;For[i=1,i<=Length[IntegerDigits[a,2]],s+=Extract[IntegerDigits[a,2],i];i++ ];PrimeQ[s]]; lst={};Do[p=Prime[n];If[BinSumPrimeQ[p],AppendTo[lst,p]],{n,4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 06 2009 *)
%t Select[Prime[Range[100]], PrimeQ[Apply[Plus, IntegerDigits[#, 2]]] &] (* _Jonathan Sondow_, Jun 09 2012 *)
%o (Haskell)
%o a081092 n = a081092_list !! (n-1)
%o a081092_list = filter ((== 1) . a010051') a052294_list
%o -- _Reinhard Zumkeller_, Nov 16 2012
%o (PARI) lista(nn) = {forprime(p=2, nn, if (isprime(hammingweight(p)), print1(p, ", ")););} \\ _Michel Marcus_, Jan 16 2015
%o (Python)
%o from sympy import isprime
%o def ok(n): return isprime(n.bit_count()) and isprime(n)
%o print([k for k in range(444) if ok(k)]) # _Michael S. Branicky_, Dec 27 2023
%Y Cf. A000040, A000120, A046704, A081093.
%Y Subsequence of A052294.
%K nonn,base
%O 1,1
%A _Reinhard Zumkeller_, Mar 05 2003
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