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A360448 Indices of primes of the form p = 2^i + 2^j + 1, i > j > 0 (A081091).

%I A360448 #21 Mar 22 2023 08:15:10
%S A360448 4,5,6,8,12,13,19,21,25,32,33,44,98,106,116,136,174,191,310,313,319,
%T A360448 565,568,1029,1470,1902,2111,3513,3518,3521,4289,6544,12426,13632,
%U A360448 15000,23001,23003,23043,23673,43395,43420,43465,45859,62947,82029,82063,91466,155612,155900,295957,564164
%N A360448 Indices of primes of the form p = 2^i + 2^j + 1, i > j > 0 (A081091).
%F A360448 a(n) = A000720(A081091(n)).
%F A360448 This sequence = { n | A000120(A000040(n)) = 3 }.
%t A360448 Position[Prime[Range[600000]], _?(DigitCount[#, 2, 1] == 3 &)] // Flatten (* _Amiram Eldar_, Mar 04 2023 *)
%t A360448 PrimePi@ Union@ Select[Flatten@ Table[2^i + 2^j + 1, {i, 0, 23}, {j, 0, i - 1}], PrimeQ] (* _Michael De Vlieger_, Mar 21 2023 *)
%o A360448 (PARI) A360448(n) = primepi(A081091(n))
%o A360448 is_A360448(n) = hammingweight(prime(n))==3
%o A360448 (Python)
%o A360448 from itertools import count, islice
%o A360448 from sympy import primepi, isprime
%o A360448 def A360448_gen(): # generator of terms
%o A360448     for i in count(2):
%o A360448         k = (1<<i)+1
%o A360448         for j in range(1,i):
%o A360448             if isprime(m := k+(1<<j)):
%o A360448                 yield primepi(m)
%o A360448 A360448_list = list(islice(A360448_gen(),20)) # _Chai Wah Wu_, Mar 21 2023
%Y A360448 Cf. A000720 (prime counting function), A081091 (primes of the form 2^i + 2^j + 1, i > j > 0), A014499 (Hamming weight of the n-th prime), A000040 (the primes), A000120 (Hamming weight).
%K A360448 nonn
%O A360448 1,1
%A A360448 _M. F. Hasler_, Mar 03 2023