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

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

Offset: 0

Author

Amiram Eldar, May 23 2024

Keywords

• nonn
• base
• hard
• more

Comments

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.

a(8) > 4*10^10.

Examples

			The iterations for the n = 0..7 are:
  n     a(n)  iterations
  -  -------  --------------------------------------------------
  0        1   1
  1        4   4 -> 3
  2        7   7 -> 4 -> 3
  3       12   12 -> 9 -> 5 ->3
  4       24   24 -> 12 -> 9 -> 5 -> 3
  5      120   120 -> 36 -> 15 -> 9 -> 5 -> 3
  6     1260   1260 -> 120 -> 36 -> 15 -> 9 -> 5 -> 3
  7  1829520   1829520 -> 1260 -> 120 -> 36 -> 15 -> 9 -> 5 -> 3
		

Crossrefs

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

Programs

Mathematica

d[n_] := d[n] = DivisorSum[n, Plus @@ IntegerDigits[#, 2] &];
f[n_] := -2 + Length@ FixedPointList[d, n];
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]

PARI

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