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A162700 Numbers k which are concatenations k = x//y such that y^2 - x^2 = k. 2

%I

%S 48,3468,10101,16128,34188,140400,190476,216513,300625,334668,416768,

%T 484848,530901,2341548,2661653,16604400,33346668,59809776,101010101,

%U 3333466668,4848484848,4989086476,18516137328,30534177388,56734244853

%N Numbers k which are concatenations k = x//y such that y^2 - x^2 = k.

%C Cases in which y has leading zeros are not considered.

%e 48 = 4//8 = 8^2 - 4^2;

%e 10101 = 10//101 = 101^2 - 10^2;

%e 16128 = 16//128 = 128^2 - 16^2.

%p Lton := proc(L) add( op(i,L)*10^(i-1),i=1..nops(L)) ; end:

%p 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)] ; if op(-1,ydgs) <> 0 then x := Lton(xdgs) ; y := Lton(ydgs) ; if y^2-x^2 = n then print(n) ; fi; fi; od: od: # _R. J. Mathar_, Jul 16 2009

%K nonn,base

%O 1,1

%A _Claudio Meller_, Jul 11 2009

%E keyword:base added, definition rephrased, values sorted by _R. J. Mathar_, Jul 16 2009

%E More terms from _Sean A. Irvine_, Nov 19 2009

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Last modified September 20 18:49 EDT 2019. Contains 327245 sequences. (Running on oeis4.)