A263351 Fixed points of A243625: integers n such that A243625(n)=n.

1, 4, 9, 18, 23, 48, 54, 60, 63, 77, 91, 92, 93, 104, 117, 126, 129, 137, 151, 152, 153, 167, 169, 214, 229, 239, 255, 256, 264, 266, 267, 270, 282, 285, 289, 293, 295, 297, 326, 342, 344, 345, 348, 350, 355, 364, 400, 420, 428, 436, 439, 440, 447, 454, 458

Offset: 1

Author

Zak Seidov, Oct 16 2015

Keywords

• nonn

Comments

Among first 1000 terms of A243625 there are 124 fixed points.

Almost certainly A243625 is a permutation of natural numbers.

And almost certainly there is no (easy) proof of it.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A243625.

Programs

Maple

with(numtheory):
b:= proc(n) is(n=1) end: h:= 2:
g:= proc(n) option remember; global h; local k, t;
      if n=1 then 1 else t:=g(n-1);
         for k from h while b(k) or bigomega(t+k)<>2
         do od; b(k):=true; while b(h) do h:=h+1 od; k
      fi
    end:
a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, a(n-1)) do
        if g(k)=k then break fi
      od: k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 17 2015

Mathematica

b[n_] := n == 1;
h = 2;
g[n_] := g[n] = Module[{k, t}, If[n == 1, 1,  t = g[n - 1]; For[k = h, b[k] || PrimeOmega[t + k] != 2, k++]; b[k] = True; While[b[h], h++]; k]];
a[n_] := a[n] = Module[{k}, For[k = 1 + If[n == 1, 0, a[n - 1]], True, k++, If[g[k] == k, Break[]]]; k];
Array[a, 100] (* Jean-François Alcover, Nov 23 2020, after Alois P. Heinz *)