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 A113659 Numbers n such that A111273(n) = n. 8
 1, 9, 25, 49, 57, 65, 81, 85, 93, 121, 133, 153, 169, 185, 201, 209, 217, 225, 253, 261, 289, 297, 301, 305, 309, 329, 333, 345, 361, 369, 381, 385, 393, 417, 441, 469, 477, 489, 497, 501, 505, 513, 525, 529, 533, 553, 561, 565, 581, 621, 625, 633, 637, 645 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A111273, A113658, A016754, A103962. Sequence in context: A075026 A339727 A339128 * A325701 A113745 A016754 Adjacent sequences:  A113656 A113657 A113658 * A113660 A113661 A113662 KEYWORD nonn AUTHOR Klaus Brockhaus, Nov 04 2005 STATUS approved

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Last modified September 28 22:34 EDT 2021. Contains 347717 sequences. (Running on oeis4.)