cp's OEIS Frontend

A071600 Numbers k such that k and prime(k) have the same number of 1's in their binary representation.

%I A071600 #23 Jul 28 2025 03:10:01
%S A071600 1,3,13,19,21,23,25,30,44,45,47,57,60,61,71,77,98,99,101,103,107,108,
%T A071600 110,118,121,125,158,159,178,179,184,186,187,188,209,215,218,221,237,
%U A071600 244,246,247,248,249,251,279,287,312,334,335,346,350,359,361,362,365
%N A071600 Numbers k such that k and prime(k) have the same number of 1's in their binary representation.
%H A071600 Amiram Eldar, <a href="/A071600/b071600.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%F A071600 a(n) = A049084(A072439(n)); A000120(a(n)) = A000120(A072439(n)). - _Reinhard Zumkeller_, Jun 17 2002
%F A071600 A090455(a(n)) = 0, A000120(a(n)) = A014499(a(n)).
%e A071600 221 = 11011101 in base 2, prime(221) = 1381 = 10101100101 in base 2, both have 6 "1's" in their binary representation, hence 221 is in the sequence.
%t A071600 Select[Range[400],DigitCount[#,2,1]==DigitCount[Prime[#],2,1]&] (* _Harvey P. Dale_, Mar 09 2015 *)
%o A071600 (PARI) for(n=1,1000,s=1; if(sum(i=1,length(binary(n)), component(binary(n),i))==sum(i=1,length(binary(prime(n))), component(binary(prime(n)),i)),print1(n,",")))
%o A071600 (PARI) is(n)=hammingweight(n)==hammingweight(prime(n)) \\ _Charles R Greathouse IV_, Mar 07 2013
%Y A071600 Cf. A000120, A014499, A033549, A049084, A072439, A090455.
%K A071600 base,easy,nonn
%O A071600 1,2
%A A071600 _Benoit Cloitre_, Jun 01 2002