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A258766 Fixed points in A256271.

%I A258766 #21 Jul 26 2024 22:09:19
%S A258766 1,2,3,26,32,34,37,49,55,62,64,74,75,76,77,164,171,189,224,273,279,
%T A258766 280,285,303,333,345,356,363,368,382,399,411,416,422,429,430,435,441,
%U A258766 453,470,472,483,494,524,539,561,566,579,580,585,603,609,621,644,662,666,674,693,704,715,737,771,777,794,803
%N A258766 Fixed points in A256271.
%C A258766 Numbers n such that A256271(n) = n.
%C A258766 From _Robert Israel_, Jul 16 2019: (Start)
%C A258766 A necessary condition for n to be in the sequence is that A256271(n)-n is even.  When A256271(n) is even, A256271(n+1) must be odd; when A256271(n) is odd, A256271(n+1) may be either even or odd, but it appears that it is nearly always even.
%C A258766 The result is that we have long intervals where A256271(n)-n is even (e.g. 3369 to 22635), in which members of this sequence are relatively common, and long intervals where A256271(n)-n is odd (e.g. 22636 to 67110) which contain no members of this sequence. (End)
%H A258766 Robert Israel, <a href="/A258766/b258766.txt">Table of n, a(n) for n = 1..1000</a>
%p A258766 Res:= 1: count:= 1: v:= 1:
%p A258766 Cands:= [$2..1000]:
%p A258766 for n from 2 do
%p A258766   found:= false;
%p A258766   for j from 1 to nops(Cands) do
%p A258766     if numtheory:-issqrfree(v + Cands[j]^2) then
%p A258766       found:= true;
%p A258766       if n = Cands[j] then Res:= Res, n; count:= count+1 fi;
%p A258766       v:= Cands[j]^2;
%p A258766       Cands:= subsop(j=NULL, Cands);
%p A258766       break
%p A258766     fi
%p A258766   od;
%p A258766   if not found then break fi;
%p A258766 od:
%p A258766 Res; # _Robert Israel_, Jul 16 2019
%o A258766 (PARI) print1(1,", ");v=[1]; n=1; while(#v<10^3, if(issquarefree(n^2+v[#v]^2)&&!vecsearch(vecsort(v), n), if(n==#v, print1(n, ", ")); n=0); n++)
%Y A258766 Cf. A121878, A167906, A256271.
%K A258766 nonn,look
%O A258766 1,2
%A A258766 _Derek Orr_, Jun 09 2015