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 A081092 Primes having in binary representation a prime number of 1's. 11
 3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 47, 59, 61, 67, 73, 79, 97, 103, 107, 109, 127, 131, 137, 151, 157, 167, 173, 179, 181, 191, 193, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 271, 283, 307, 313, 331, 367, 379, 397, 409, 419, 421, 431, 433, 439, 443 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Same as primes with prime binary digit sum. Primes with prime decimal digit sum are A046704. 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 A049084(A000120(a(n))) > 0; A081091, A000215 and A081093 are subsequences. 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. 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 CROSSREFS Cf. A000040, A000120, A046704, A081093. Subsequence of A052294. Sequence in context: A038604 A155026 A295705 * A291360 A269326 A163422 Adjacent sequences:  A081089 A081090 A081091 * A081093 A081094 A081095 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Mar 05 2003 STATUS approved

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Last modified June 24 05:09 EDT 2021. Contains 345416 sequences. (Running on oeis4.)