A358055 a(n) is the least m such that A358052(m,k) = n for some k.
1, 2, 5, 8, 14, 20, 32, 38, 59, 59, 63, 116, 122, 158, 158, 218, 278, 278, 402, 548, 642, 642, 642, 642, 642, 1062, 1062, 1668, 2474, 2690, 2690, 2690, 2690, 2690, 3170, 3170, 3170, 3170, 3170, 3170, 3170, 9260, 9260, 9260, 9788, 9788, 11772, 11942, 11942, 11942, 11942, 11942
Offset: 1
Keywords
Examples
a(4) = 8 because A358052(8,6) = 4 and this is the first appearance of 4 in A358052. Thus the map x -> floor(8/x) + (8 mod x) starting at 6 produces 4 distinct values before repeating: 6 -> 3 -> 4 -> 2 -> 4.
Programs
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Maple
f:= proc(n, k) local x, S, count; S:= {k}; x:= k; for count from 1 do x:= iquo(n, x) + irem(n, x); if member(x, S) then return count fi; S:= S union {x}; od end proc: V:= Vector(50): count:= 0: for n from 1 while count < 50 do for k from 1 to n do v:= f(n,k); if v <= 50 and V[v] = 0 then V[v]:= n; count:= count+1; fi od od: convert(V,list); -
Mathematica
f[n_, k_] := Module[{x, S, count}, S = {k}; x = k; For[count = 1, True, count++, x = Quotient[n, x] + Mod[n, x]; If[MemberQ[S, x], Return@count]; S = S~Union~{x}]]; V = Table[0, {vmax = 40}]; count = 0; For[n = 1, count < vmax, n++, For[k = 1, k <= n, k++, v = f[n, k]; If[v <= vmax && V[[v]] == 0, Print[n]; V[[v]] = n; count++]]]; V (* Jean-François Alcover, Mar 12 2024, after Maple code *)
Comments