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%I #15 Aug 03 2023 03:44:22
%S 2,5,41,67,73,83,97,113,193,197,211,269,281,283,353,389,521,523,547,
%T 563,587,593,601,647,661,691,929,937,1061,1063,1097,1109,1117,1123,
%U 1289,1319,1361,1381,1489,1549,1559,1567,1571,1579,1597,1801,1873,2069
%N Primes prime(k) such that the number of binary 1's in prime(k) equals the number of binary 1's in k.
%H Amiram Eldar, <a href="/A072439/b072439.txt">Table of n, a(n) for n = 1..10000</a>
%F A000120(a(n)) = A000120(A071600(n)) = A014499(n).
%F A090455(A049084(a(n))) = 0.
%F a(n) = A000040(A071600(n)).
%e In binary representation 13 and A000040(13)=41 have three 1's: 13='1101' and 41='101001', therefore 41 is a term.
%t Prime[Select[Range[400], DigitCount[#, 2, 1] == DigitCount[Prime[#], 2, 1] &]] (* _Amiram Eldar_, Aug 03 2023 *)
%o (PARI) isok(p) = isprime(p) && ((hammingweight(p) == hammingweight(primepi(p)))); \\ _Michel Marcus_, Jun 14 2021
%Y Cf. A000040, A000120, A014499, A033548, A049084, A071600, A090455.
%K nonn,base
%O 1,1
%A _Reinhard Zumkeller_, Jun 17 2002