A162463 Numbers k which are concatenations k=x//y such that x^2 + y^2 is a multiple of k.

101, 137, 202, 274, 292, 303, 404, 505, 606, 657, 707, 808, 909, 1233, 2466, 3577, 3699, 8833, 9901, 10100, 16577, 17666, 20200, 26499, 30300, 40400, 49457, 50500, 60600, 70700, 80800, 90900, 99937, 100010, 110011, 120012, 130013, 140014, 150015, 160016, 170017

Offset

1,1

Comments

Concatenations with x=0 or y=0 or that allow y with leading zeros are not taken into account.

Links

Table of n, a(n) for n=1..41.

Example

274 is a term because 2^2 + 74^2 = 4 + 5476 = 5480 = 20*274.
2466 is a term because 24^2 + 66^2 = 576+4356 = 4932 = 2*2466.
110011 is a term because 1100^2 + 11^2 = 11*110011.

Maple

Lton := proc(L) add(op(i, L)*10^(i-1), i=1..nops(L)) ; end:
isA162463 := proc(n) dgs := convert(n, base, 10) ; for spl from 1 to nops(dgs)-1 do y := Lton([op(1..spl, dgs)]) ; x := Lton([op(spl+1..nops(dgs), dgs)]) ; if x<> 0 and y <> 0 and op(spl, dgs) <> 0 and (x^2+y^2) mod n = 0 then RETURN(true) ; fi; od: RETURN(false) ; end:
for n from 1 to 1000000 do if isA162463(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Jul 10 2009

Crossrefs

Sequence in context: A158089 A104946 A272075 * A035790 A139489 A358737

Adjacent sequences: A162460 A162461 A162462 * A162464 A162465 A162466

Keyword

nonn,base

Author

Claudio Meller, Jul 04 2009

Extensions

Missing terms inserted by R. J. Mathar, Jul 10 2009

Status

approved