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

%I A263351 #17 Nov 23 2020 17:09:55
%S A263351 1,4,9,18,23,48,54,60,63,77,91,92,93,104,117,126,129,137,151,152,153,
%T A263351 167,169,214,229,239,255,256,264,266,267,270,282,285,289,293,295,297,
%U A263351 326,342,344,345,348,350,355,364,400,420,428,436,439,440,447,454,458
%N A263351 Fixed points of A243625: integers n such that A243625(n)=n.
%C A263351 Among first 1000 terms of A243625 there are 124 fixed points.
%C A263351 Almost certainly A243625 is a permutation of natural numbers.
%C A263351 And almost certainly there is no (easy) proof of it.
%H A263351 Alois P. Heinz, <a href="/A263351/b263351.txt">Table of n, a(n) for n = 1..10000</a>
%p A263351 with(numtheory):
%p A263351 b:= proc(n) is(n=1) end: h:= 2:
%p A263351 g:= proc(n) option remember; global h; local k, t;
%p A263351       if n=1 then 1 else t:=g(n-1);
%p A263351          for k from h while b(k) or bigomega(t+k)<>2
%p A263351          do od; b(k):=true; while b(h) do h:=h+1 od; k
%p A263351       fi
%p A263351     end:
%p A263351 a:= proc(n) option remember; local k;
%p A263351       for k from 1+`if`(n=1, 0, a(n-1)) do
%p A263351         if g(k)=k then break fi
%p A263351       od: k
%p A263351     end:
%p A263351 seq(a(n), n=1..100);  # _Alois P. Heinz_, Oct 17 2015
%t A263351 b[n_] := n == 1;
%t A263351 h = 2;
%t A263351 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]];
%t A263351 a[n_] := a[n] = Module[{k}, For[k = 1 + If[n == 1, 0, a[n - 1]], True, k++, If[g[k] == k, Break[]]]; k];
%t A263351 Array[a, 100] (* _Jean-François Alcover_, Nov 23 2020, after _Alois P. Heinz_ *)
%Y A263351 Cf. A243625.
%K A263351 nonn
%O A263351 1,2
%A A263351 _Zak Seidov_, Oct 16 2015