A376619 - OEIS

%I #7 Sep 30 2024 12:50:19

%S 3,21,345,10625,74375,860625,84189105,1599592995,23993894925

%N a(n) is the least odd number k such that A376615(k) = n, or -1 if no such number exists.

%C Without the restriction to odd numbers the corresponding sequence is 3*2^(n-1) = A007283(n-1).

%C All the terms above 3 are odd binary Niven numbers (A144302).

%C a(10) > 10^13, if it exists.

%e   n | The n iterations

%e   --+------------------------------------------------------

%e   1 | 3 -> 3/2

%e   2 | 21 -> 7 -> 7/3

%e   3 | 345 -> 69 -> 23 -> 23/4

%e   4 | 10625 -> 2125 -> 425 -> 85 -> 85/4

%e   5 | 74375 -> 10625 -> 2125 -> 425 -> 85 -> 85/4

%e   6 | 860625 -> 95625 -> 10625 -> 2125 -> 425 -> 85 -> 85/4

%t s[n_] := s[n] = Module[{bw = DigitCount[n, 2, 1]}, If[bw == 1, 0, If[!Divisible[n, bw], 1, 1 + s[n/bw]]]]; seq[len_] := Module[{v = Table[0, {len}], c = 0, k = 3, i}, While[c < len, i = s[k]; If[v[[i]] == 0, c++; v[[i]] = k]; k += 2]; v]; seq[5]

%o (PARI) s(n) = {my(w = hammingweight(n)); if(w == 1, 0, if(n % w, 1, 1 + s(n/w)));}

%o lista(len) = {my(v = vector(len), c = 0, k = 3, i); while(c < len, i = s(k); if(v[i] == 0, c++; v[i] = k); k += 2); v;}

%Y Cf. A007283, A049445, A144302, A376615, A376616, A376617.

%K nonn,base,more

%O 1,1

%A _Amiram Eldar_, Sep 30 2024