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

48, 3468, 10101, 16128, 34188, 140400, 190476, 216513, 300625, 334668, 416768, 484848, 530901, 2341548, 2661653, 16604400, 33346668, 59809776, 101010101, 3333466668, 4848484848, 4989086476, 18516137328, 30534177388, 56734244853

Offset: 1

Author

Claudio Meller, Jul 11 2009

Keywords

• nonn
• base

Comments

Cases in which y has leading zeros are not considered.

Examples

			48 = 4//8 = 8^2 - 4^2;
10101 = 10//101 = 101^2 - 10^2;
16128 = 16//128 = 128^2 - 16^2.
		

Programs

Maple

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

Extensions

keyword:base added, definition rephrased, values sorted by R. J. Mathar, Jul 16 2009

More terms from Sean A. Irvine, Nov 19 2009