A321226 - OEIS

%I #29 Nov 13 2018 12:52:32

%S 2,3,14,5,28,59,22,7,30,115,238,117,44,91,30,9,56,123,462,229,476,955,

%T 470,119,46,179,366,181,60,123,38,11,58,227,494,245,924,1851,918,231,

%U 478,1907,3822,1909,940,1883,478,233,88,187,718,357,732,1467,726,183

%N Describe the binary representation of n in binary and convert back to decimal.

%C This sequence is a binary variant of the "Look and Say" sequence A045918.

%C There is only one fixed point: a(7) = 7.

%H Rémy Sigrist, <a href="/A321226/b321226.txt">Table of n, a(n) for n = 0..8192</a>

%F a(2^n - 1) = 2*n + 1 for any n > 0.

%F a(4*n + 1) = 4*a(2*n) + 3 for any n > 0.

%F a(4*n + 2) = 4*a(2*n + 1) + 2 for any n >= 0.

%F a(A020330(2*n)) = A020330(a(2*n)) for any n > 0.

%F a(A049190(n)) = A049190(n+1) for any n > 0.

%e For n = 67:

%e - the binary representation of 67 is "1000011",

%e - we see, in binary: "1" "1", "100" "0", "10" "1",

%e - hence the binary representation of a(67) is "111000101",

%e - and a(67) = 453 in decimal.

%o (PARI) a(n, b=2) = if (n==0, return (b)); my (d=digits(b*n, b), v=0, w=0); d[#d] = -1; for (i=1, #d-1, w++; if (d[i]!=d[i+1], v = b*(v*b^#digits(w, b) + w) + d[i]; w = 0)); v

%Y Cf. A020330, A045918, A049190.

%K nonn,base

%O 0,1

%A _Rémy Sigrist_, Nov 10 2018