cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A376619 a(n) is the least odd number k such that A376615(k) = n, or -1 if no such number exists.

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%I A376619 #7 Sep 30 2024 12:50:19
%S A376619 3,21,345,10625,74375,860625,84189105,1599592995,23993894925
%N A376619 a(n) is the least odd number k such that A376615(k) = n, or -1 if no such number exists.
%C A376619 Without the restriction to odd numbers the corresponding sequence is 3*2^(n-1) = A007283(n-1).
%C A376619 All the terms above 3 are odd binary Niven numbers (A144302).
%C A376619 a(10) > 10^13, if it exists.
%e A376619   n | The n iterations
%e A376619   --+------------------------------------------------------
%e A376619   1 | 3 -> 3/2
%e A376619   2 | 21 -> 7 -> 7/3
%e A376619   3 | 345 -> 69 -> 23 -> 23/4
%e A376619   4 | 10625 -> 2125 -> 425 -> 85 -> 85/4
%e A376619   5 | 74375 -> 10625 -> 2125 -> 425 -> 85 -> 85/4
%e A376619   6 | 860625 -> 95625 -> 10625 -> 2125 -> 425 -> 85 -> 85/4
%t A376619 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 A376619 (PARI) s(n) = {my(w = hammingweight(n)); if(w == 1, 0, if(n % w, 1, 1 + s(n/w)));}
%o A376619 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 A376619 Cf. A007283, A049445, A144302, A376615, A376616, A376617.
%K A376619 nonn,base,more
%O A376619 1,1
%A A376619 _Amiram Eldar_, Sep 30 2024