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

147, 528, 729, 1617, 8019, 13467, 71289, 91091, 130896, 310497, 350268, 970299, 1010100, 1016127, 1034187, 1140399, 1190475, 1216512, 1300624, 1334667, 1360167, 1416767, 1484847, 1530900, 2020200, 2032254, 2068374, 2280798

Offset: 1

Author

Claudio Meller, Jul 11 2009

Keywords

• nonn
• base

Comments

Cases in which y has leading zeros or y >= x are not considered.

Examples

			147 = 14//7, 14^2 - 7^2 = 1*147;
528 = 52//8, 52^2 - 8^2 = 5*528;
729 = 72//9, 72^2 - 9^2 = 7*729.
		

Crossrefs

Cf. A162700.

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 x > y then if (x^2-y^2) mod n = 0 then print(n) ; fi; fi; fi;
od: od: # R. J. Mathar, Jul 16 2009

Extensions

keyword:base added, definition rephrased, 3 terms added by R. J. Mathar, Jul 16 2009

More terms from Sean A. Irvine, Apr 15 2010