A394533 - OEIS

%I #9 Mar 29 2026 12:42:23

%S 1,2,3,4,10,6,7,8,36,20,42,12,26,14,15,16,136,72,292,40,164,84,170,24,

%T 100,52,106,28,58,30,31,32,528,272,2184,144,1160,584,2340,80,648,328,

%U 1316,168,676,340,682,48,392,200,804,104,420,212,426,56,228,116,234

%N Binary expansion of a(n) obtained from binary expansion of n with increased number of zeros separated by every next 1 by total number of zeros lying from the left side of selected 1.

%C Permutation of A225620.

%e Binary expansion of n = 41 is 1(0)1(00)1(), then binary expansion of a(n) is 1(0)1(00,0)1(00,0).

%o (PARI) a(n) = my(A = 2*n+1, B = 0, C = 0); forstep(k=logint(n,2), 0, -1, if(bittest(A,k), B = (1+B<<1)<<C, C++)); B

%o (Python)

%o def a(n: int) -> int:

%o     C, B, A = 0, 0, 2*n + 1

%o     for k in range(n.bit_length() - 1, -1, -1):

%o         if (A >> k) & 1: B = (1 + (B << 1)) << C

%o         else: C += 1

%o     return B

%o print([a(n) for n in range(1, 60)])  # _Peter Luschny_, Mar 28 2026

%Y Cf. A125106, A225620.

%K nonn,base,easy

%O 1,2

%A _Mikhail Kurkov_, Mar 24 2026