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Fixed points of A243625: integers n such that A243625(n)=n.
1

%I #17 Nov 23 2020 17:09:55

%S 1,4,9,18,23,48,54,60,63,77,91,92,93,104,117,126,129,137,151,152,153,

%T 167,169,214,229,239,255,256,264,266,267,270,282,285,289,293,295,297,

%U 326,342,344,345,348,350,355,364,400,420,428,436,439,440,447,454,458

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

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

%C Almost certainly A243625 is a permutation of natural numbers.

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

%H Alois P. Heinz, <a href="/A263351/b263351.txt">Table of n, a(n) for n = 1..10000</a>

%p with(numtheory):

%p b:= proc(n) is(n=1) end: h:= 2:

%p g:= proc(n) option remember; global h; local k, t;

%p if n=1 then 1 else t:=g(n-1);

%p for k from h while b(k) or bigomega(t+k)<>2

%p do od; b(k):=true; while b(h) do h:=h+1 od; k

%p fi

%p end:

%p a:= proc(n) option remember; local k;

%p for k from 1+`if`(n=1, 0, a(n-1)) do

%p if g(k)=k then break fi

%p od: k

%p end:

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Oct 17 2015

%t b[n_] := n == 1;

%t h = 2;

%t 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 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 Array[a, 100] (* _Jean-François Alcover_, Nov 23 2020, after _Alois P. Heinz_ *)

%Y Cf. A243625.

%K nonn

%O 1,2

%A _Zak Seidov_, Oct 16 2015