A334245 Let S = A061228, T = A070229, and F = S o T (where o denotes composition). Then a(n) is the least number in the intersection of the sequences F^k(n) and F^k(S(n)), k>=0, or the intersection of the sequences T(F^k(n)) and T(F^k(S(n))), k>=0, or 0 if these intersections are empty.

12, 12, 12, 15, 12, 30, 15, 21, 15, 77, 21, 77, 30, 77, 30, 77, 30, 57, 77, 30, 77, 91, 77, 77, 77, 77, 35, 105, 77, 133, 77, 91, 77, 60, 77, 111, 57, 77, 77, 133, 77, 165, 91, 65, 91, 147, 60, 105, 65, 70, 65, 165, 77, 105, 105, 91, 105, 180, 133, 231, 133, 91, 105, 105, 105, 234, 105, 147, 91

Offset

2,1

Comments

60420 >= a(n) > 0 for n <= 6042, but either a(6043) = 0 or a(6043) > 10^30.

If p is prime, a(p) = a(2*p).

From n = 5, 55, 2, 24, 245, ... begin successive strings of exactly 1, 2, 3, 4, 5, ... identical merging points that are: 15, 105, 12, 77, 713, ... . - Bernard Schott, Jul 04 2020

Links

Robert Israel, Table of n, a(n) for n = 2..6042

A. Sada et al., Will this pattern continue, Discussion in SeqFan mailing list, Apr 2020.

Bernard and Blandine Schott, Network with terms < 100.

Formula

a(2^m+2) = a(2^m). - Bernard Schott, Jun 27 2020

Example

For n=5, 15 = T(F(5)) = T(S(5)) so a(5) = 15.
For n=6, 12 = F(6) = F(S(6)) so a(6) = 12.
For n=10, 15 = T(10) = T(F(10)) so a(10) = 15.

Maple

S:= x -> x + min(numtheory:-factorset(x)):
T:= x -> x + max(numtheory:-factorset(x)):
f:= proc(n) local s, t, i, j, ct;
  s:= S(n); i:= 0; t:= T(n); j:= 1;
  for ct from 1 to 1000 do
    if s = t and i=j then return s fi;
    if s <= t then
      if i = 0 then s:= T(s); i:= 1
      else s:= S(s); i:= 0
      fi
    elif j = 0 then t:= T(t); j:= 1
    else t:= S(t); j:= 0
    fi
  od;
  0
end proc:
map(f, [$2..100]);

Mathematica

S[x_] := x + FactorInteger[x][[1, 1]];
T[x_] := x + FactorInteger[x][[-1, 1]];
f[n_] := Module[{s = S[n], t = T[n], i = 0, j = 1, ct}, For[ct = 1, ct <= 1000, ct++, If[s == t && i == j, Return[s]]; If[s <= t, If[i == 0, s = T[s]; i = 1, s = S[s]; i = 0], If[j == 0, t = T[t]; j = 1, t = S[t]; j = 0]]]; 0];
f /@ Range[2, 100] (* Jean-François Alcover, Aug 15 2020, after Maple *)

Crossrefs

Cf. A061228, A070229, A335859.

Sequence in context: A113595 A109053 A186100 * A134324 A268914 A056627

Adjacent sequences: A334242 A334243 A334244 * A334246 A334247 A334248

Keyword

nonn,look

Author

Ali Sada and Robert Israel, Apr 19 2020

Status

approved