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A162701 Numbers k which are concatenations k = x//y such that x^2 - y^2 is a multiple of k.

%I A162701 #7 Mar 01 2019 23:34:09
%S A162701 147,528,729,1617,8019,13467,71289,91091,130896,310497,350268,970299,
%T A162701 1010100,1016127,1034187,1140399,1190475,1216512,1300624,1334667,
%U A162701 1360167,1416767,1484847,1530900,2020200,2032254,2068374,2280798
%N A162701 Numbers k which are concatenations k = x//y such that x^2 - y^2 is a multiple of k.
%C A162701 Cases in which y has leading zeros or y >= x are not considered.
%e A162701 147 = 14//7, 14^2 - 7^2 = 1*147;
%e A162701 528 = 52//8, 52^2 - 8^2 = 5*528;
%e A162701 729 = 72//9, 72^2 - 9^2 = 7*729.
%p A162701 Lton := proc(L) add( op(i,L)*10^(i-1),i=1..nops(L)) ; end:
%p A162701 for n from 10 do dgs := convert(n,base,10) ; for spli from 1 to nops(dgs)-1 do ydgs := [op(1..spli,dgs)] ; xdgs := [op(spli+1..nops(dgs),dgs)] ;
%p A162701 if op(-1,ydgs) <> 0 then x := Lton(xdgs) ; y := Lton(ydgs) ; if x > y then if (x^2-y^2) mod n = 0 then print(n) ; fi; fi; fi;
%p A162701 od: od: # _R. J. Mathar_, Jul 16 2009
%Y A162701 Cf. A162700.
%K A162701 nonn,base
%O A162701 1,1
%A A162701 _Claudio Meller_, Jul 11 2009
%E A162701 keyword:base added, definition rephrased, 3 terms added by _R. J. Mathar_, Jul 16 2009
%E A162701 More terms from _Sean A. Irvine_, Apr 15 2010