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 A373094 a(n) is the least number k such that A373092(k) = n. 1

%I #6 May 24 2024 03:28:16

%S 1,4,7,12,24,120,1260,1829520

%N a(n) is the least number k such that A373092(k) = n.

%C a(n) is the least number k such that the number of iterations of the map x -> A093653(x) required to reach from k to a fixed point is n.

%C a(8) > 4*10^10.

%e The iterations for the n = 0..7 are:

%e n a(n) iterations

%e - ------- --------------------------------------------------

%e 0 1 1

%e 1 4 4 -> 3

%e 2 7 7 -> 4 -> 3

%e 3 12 12 -> 9 -> 5 ->3

%e 4 24 24 -> 12 -> 9 -> 5 -> 3

%e 5 120 120 -> 36 -> 15 -> 9 -> 5 -> 3

%e 6 1260 1260 -> 120 -> 36 -> 15 -> 9 -> 5 -> 3

%e 7 1829520 1829520 -> 1260 -> 120 -> 36 -> 15 -> 9 -> 5 -> 3

%t d[n_] := d[n] = DivisorSum[n, Plus @@ IntegerDigits[#, 2] &];

%t f[n_] := -2 + Length@ FixedPointList[d, n];

%t seq[len_] := Module[{s = Table[0, {len}], c = 0, i, n = 1}, While[c < len, i = f[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[7]

%o (PARI) f(n) = {my(c = 0); while(6 % n, n = sumdiv(n, d, hammingweight(d)); c++); c;}

%o lista(len) = {my(s = vector(len), c = 0, i, n = 1); while(c < len, i = f(n) + 1; if(i <= len && s[i] == 0, c++; s[i] = n); n++); s;}

%Y Cf. A093653, A095347 (decimal analog), A373092.

%K nonn,base,hard,more

%O 0,2

%A _Amiram Eldar_, May 23 2024

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Last modified August 15 11:39 EDT 2024. Contains 375173 sequences. (Running on oeis4.)