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A162701 Numbers k which are concatenations k = x//y such that x^2 - y^2 is a multiple of k. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

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.

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

CROSSREFS

Cf. A162700.

Sequence in context: A325608 A255103 A184542 * A063701 A261939 A251107

Adjacent sequences:  A162698 A162699 A162700 * A162702 A162703 A162704

KEYWORD

nonn,base

AUTHOR

Claudio Meller, Jul 11 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

STATUS

approved

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Last modified September 20 18:52 EDT 2019. Contains 327245 sequences. (Running on oeis4.)