cp's OEIS Frontend

A359259 a(n) is the least k such that A359194(k) = A032766(n).

%I A359259 #7 Dec 24 2022 11:12:31
%S A359259 1,0,4,9,3,8,18,7,17,6,16,37,15,36,14,35,13,34,12,33,11,32,74,31,73,
%T A359259 30,72,29,71,28,70,27,69,26,68,25,67,24,66,23,65,22,64,149,63,148,62,
%U A359259 147,61,146,60,145,59,144,58,143,57,142,56,141,55,140,54,139
%N A359259 a(n) is the least k such that A359194(k) = A032766(n).
%C A359259 The binary expansion of numbers m such that A359194(m) = A032766(n):
%C A359259 - starts with zero or more occurrences of "10",
%C A359259 - followed by a "0" when the binary expansion of a(n) starts with zero or more occurrences of "10" followed by "11",
%C A359259 - ends with the binary expansion of a(n) (assuming that 0 has an empty binary expansion).
%e A359259 The first terms, alongside the binary expansions of A032766(n) and a(n), are:
%e A359259   n   a(n)  bin(A032766(n))  bin(a(n))
%e A359259   --  ----  ---------------  ---------
%e A359259    0     1                0          1
%e A359259    1     0                1          0
%e A359259    2     4               11        100
%e A359259    3     9              100       1001
%e A359259    4     3              110         11
%e A359259    5     8              111       1000
%e A359259    6    18             1001      10010
%e A359259    7     7             1010        111
%e A359259    8    17             1100      10001
%e A359259    9     6             1101        110
%e A359259   10    16             1111      10000
%e A359259   11    37            10000     100101
%o A359259 (PARI) a(n) = { if (n<=1, return (1-n), n+=n\2; for (x=2+exponent(n), oo, my (k=bitneg(n,x)); if (k%3==0, return (k/3)))) }
%Y A359259 Cf. A032766, A359194.
%K A359259 nonn,base
%O A359259 0,3
%A A359259 _Rémy Sigrist_, Dec 23 2022