cp's OEIS Frontend

A364295 Numbers k such that A292943(k) = A292944(k).

%I A364295 #11 Jul 27 2023 15:31:17
%S A364295 1,2,3,4,6,8,9,12,16,18,24,32,36,45,48,64,72,90,96,128,144,165,180,
%T A364295 189,192,256,288,330,360,378,384,512,576,660,720,756,768,1024,1152,
%U A364295 1320,1440,1512,1536,2048,2304,2640,2880,3024,3072,4096,4608,5280,5760,6048,6144,8192,9216,10560,11520,12096,12288,16384
%N A364295 Numbers k such that A292943(k) = A292944(k).
%C A364295 If n is present, then 2*n is also present, and vice versa.
%C A364295 A007283 is included as a subsequence, because it gives the known fixed points of map n -> A163511(n).
%o A364295 (PARI)
%o A364295 A004754(n) = (n+(1<<(#binary(n)-1)));
%o A364295 A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); };
%o A364295 A292272(n) = (n - bitand(n,n\2));
%o A364295 A292944(n) = (A292272(A004754(n)) - 2*A053644(n));
%o A364295 A054429(n) = ((3<<#binary(n\2))-n-1);
%o A364295 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A364295 A243071(n) = if(n<=2, n-1, A054429(A156552(n)));
%o A364295 A292943(n) = A292944(A243071(n));
%o A364295 isA364295(n) = (A292943(n)==A292944(n));
%Y A364295 Cf. A163511, A243071, A292943, A292944.
%Y A364295 Subsequences: A000079, A007283, A029744, A364296 (odd terms).
%Y A364295 Cf. also A364494, A364496.
%K A364295 nonn
%O A364295 1,2
%A A364295 _Antti Karttunen_, Jul 26 2023