cp's OEIS Frontend

A165086 Consider the base-7 Kaprekar map x->K(x) described in A165071. Sequence gives the smallest number that belongs to a cycle of length n under repeated iteration of this map, or -1 if there is no cycle of length n.

%I A165086 #6 Jul 22 2025 07:19:49
%S A165086 0,144,1068,9458722410775248,9936,55500,65945195409025452
%N A165086 Consider the base-7 Kaprekar map x->K(x) described in A165071. Sequence gives the smallest number that belongs to a cycle of length n under repeated iteration of this map, or -1 if there is no cycle of length n.
%C A165086 Known values (to 100 base-7 digits):
%C A165086 a(1) = 0 (base 10) = 0 (base 7)
%C A165086 a(2) = 144 (base 10) = 264 (base 7)
%C A165086 a(3) = 1068 (base 10) = 3054 (base 7)
%C A165086 a(4) = 9458722410775248 (base 10) = 5544222066654442212 (base 7)
%C A165086 a(5) = 9936 (base 10) = 40653 (base 7)
%C A165086 a(6) = 55500 (base 10) = 320544 (base 7)
%C A165086 a(7) = 65945195409025452 (base 10) = 55332221066554443312 (base 7)
%C A165086 a(9) = 419850417612 (base 10) = 42222166444443 (base 7)
%C A165086 a(10) = 114965566537586468276798389479111631100827277423731225926928273344 (base 10) = 65444444444444444444444443066666666666666666666666532222222222222222222222211 (base 7)
%C A165086 a(11) = 31412208 (base 10) = 530666532 (base 7)
%C A165086 a(12) = 26884299308652 (base 10) = 5443216666443222 (base 7)
%C A165086 a(13) = 894060461610805641013834968 (base 10) = 54444444322106666665544322222222 (base 7)
%C A165086 a(14) = 1591271424672409468790707489057394638817384701224062547077367141620193382944 (base 10) = 65444444444444444444444444444306666666666666666666666666665322222222222222222222222222211 (base 7)
%C A165086 a(17) = 107837050564847832079804652808012 (base 10) = 55444444332221110666655554443322222212 (base 7)
%C A165086 a(24) = 7598644111289477155212 (base 10) = 54443222221066554444432222 (base 7)
%C A165086 a(25) = 18244344524504743400068812 (base 10) = 544432222222106655444444432222 (base 7)
%H A165086 <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a>
%Y A165086 Cf. A165071, A165075, A165076, A165078, A165080, A165082.
%Y A165086 In other bases: A153881 (base 2), A165008 (base 3), A165028 (base 4), A165047 (base 5), A165067 (base 6), A165106 (base 8), A165126 (base 9), A151959 (base 10).
%K A165086 base,nonn
%O A165086 1,2
%A A165086 _Joseph Myers_, Sep 04 2009