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%I #7 Feb 26 2019 03:38:20
%S 101,137,202,274,292,303,404,505,606,657,707,808,909,1233,2466,3577,
%T 3699,8833,9901,10100,16577,17666,20200,26499,30300,40400,49457,50500,
%U 60600,70700,80800,90900,99937,100010,110011,120012,130013,140014,150015,160016,170017
%N Numbers k which are concatenations k=x//y such that x^2 + y^2 is a multiple of k.
%C Concatenations with x=0 or y=0 or that allow y with leading zeros are not taken into account.
%e 274 is a term because 2^2 + 74^2 = 4 + 5476 = 5480 = 20*274.
%e 2466 is a term because 24^2 + 66^2 = 576+4356 = 4932 = 2*2466.
%e 110011 is a term because 1100^2 + 11^2 = 11*110011.
%p Lton := proc(L) add(op(i,L)*10^(i-1),i=1..nops(L)) ; end:
%p 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:
%p for n from 1 to 1000000 do if isA162463(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Jul 10 2009
%K nonn,base
%O 1,1
%A _Claudio Meller_, Jul 04 2009
%E Missing terms inserted by _R. J. Mathar_, Jul 10 2009