OFFSET
1,1
COMMENTS
Same as primes with prime binary digit sum.
Primes with prime decimal digit sum areA046704.
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
LINKS
Reinhard Zumkeller,Table of n, a(n) for n = 1..10000
G. Harman,Counting Primes whose Sum of Digits is Prime,J. Integer Seq., 15 (2012), Article 12.2.2.
EXAMPLE
15th prime = 47 = '101111' with five 1's, therefore 47 is in the sequence.
MAPLE
q:= n-> isprime(n) and isprime(add(i, i=Bits[Split](n))):
select(q, [$1..500])[]; #Alois P. Heinz,Sep 28 2023
MATHEMATICA
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 *)
Select[Prime[Range[100]], PrimeQ[Apply[Plus, IntegerDigits[#, 2]]] &] (*Jonathan Sondow,Jun 09 2012 *)
PROG
(Haskell)
a081092 n = a081092_list!! (n-1)
a081092_list = filter ((== 1). a010051') a052294_list
--Reinhard Zumkeller,Nov 16 2012
(PARI) lista(nn) = {forprime(p=2, nn, if (isprime(hammingweight(p)), print1(p, "," )); ); } \\Michel Marcus,Jan 16 2015
(Python)
from sympy import isprime
def ok(n): return isprime(n.bit_count()) and isprime(n)
print([k for k in range(444) if ok(k)]) #Michael S. Branicky,Dec 27 2023
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller,Mar 05 2003
STATUS
approved