|
%I #35 Nov 03 2023 15:35:30
%S 2,43,41,139,269,773,1049,2309,4357,8737,16673,34819,66569,139393,
%T 279553,589829,1051649,2621569,4260097,9437189,17039489,33817601,
%U 67649537,167903233,269484097,545260033,1074267137,2155872769,4311760897,12884901893,17184063521
%N The n-th prime with n 0-bits in its binary expansion.
%H Alois P. Heinz, <a href="/A236695/b236695.txt">Table of n, a(n) for n = 1..500</a> (first 40 terms from Charles R Greathouse IV)
%e Primes p(k) such that
%e A035103(p(k)) = 0: 3, 7, 31, 127, 8191,...
%e A035103(p(k)) = 1: 2, 5, 11, 13, 23, 29,...
%e A035103(p(k)) = 2: 19, 43, 53, 79, 103, 107,...
%e A035103(p(k)) = 3: 17, 37, 41, 71, 83, 89, 101,...
%e A035103(p(k)) = 4: 67, 73, 97, 139, 149, 163,...
%e A035103(p(k)) = 5: 131, 137, 193, 263, 269, 277,...
%o (PARI) nz(n)=#binary(n)-hammingweight(n)
%o a(n)=my(k=n);forprime(p=2,,if(nz(p)==n&&k--==0,return(p))) \\ _Charles R Greathouse IV_, Feb 04 2014
%Y Cf. A066195 (least prime having n zeros in binary), A236513 (the n-th prime with n 1-bits in its binary expansion).
%K nonn,base,less
%O 1,1
%A _Irina Gerasimova_, Jan 30 2014
%E New name from _Ralf Stephan_ and _Charles R Greathouse IV_, Feb 04 2014
%E a(14)-a(27) from _Charles R Greathouse IV_, Feb 04 2014
%E a(28)-a(31) from _Giovanni Resta_, Feb 04 2014
|
