OFFSET
1,2
COMMENTS
Fixed-points of the permutation of the natural numbers given in A111273.
Most odd squares appear to be in this sequence, e.g. 1,9,25,49,81,121,139,... The smallest odd square not appearing is 39^2=1521. - John W. Layman, Nov 10 2005. (See A103962.)
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..1000
Enrique Navarrete, Daniel Orellana, Finding Prime Numbers as Fixed Points of Sequences, arXiv:1907.10023 [math.NT], 2019.
EXAMPLE
The first nine terms of A111273 are {1,3,2,5,15,7,4,6,9,...}, so 1 and 9 are fixed-points.
MATHEMATICA
Select[MapIndexed[{First@ #2, #1} &, Nest[Function[{a, D}, Append[a, SelectFirst[D, FreeQ[a, #] &] /. k_ /; ! IntegerQ@ k -> Nothing]] @@ {#, Divisors@ PolygonalNumber[Length@ # + 1]} &, {1}, 645] ], SameQ @@ # &][[All, 1]] (* Michael De Vlieger, Oct 03 2019 *)
PROG
(PARI) {m=650; v=Set([]); w=[]; for(k=1, m, d=divisors(k*(k+1)/2); j=1; while(setsearch(v, d[j])>0, j++); a=d[j]; v=setunion(v, Set(a)); w=concat(w, a)); for(n=1, m, if(n==w[n], print1(n, ", ")))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Nov 04 2005
STATUS
approved