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%I #7 Apr 13 2019 11:22:18
%S 24,27,37,48,108,111,117,143,147,148,189,216,222,231,234,243,252,259,
%T 264,273,286,288,296,297,333,351,416,429,432,444,448,462,468,481,486,
%U 525,555,585,616,648,666,693,729,777,814,819,832,858,864,888,896,999
%N Numbers k = x//y which are a concatenation of x and y such that x^3 + y^3 is a multiple of k.
%C Splicing of k such that y has leading zero digits is not admitted.
%e 24 = 2//4 is listed because 2^3 + 4^3 = 72 = 3*24.
%e 117 = 1//17 is listed because 1^3 + 17^3 = 1 + 4913 = 4914 = 42*117.
%p Lton := proc(L) add(op(i,L)*10^(i-1),i=1..nops(L)) ; end:
%p isA162465 := proc(n) dgs := convert(n,base,10) ; for b from 1 to nops(dgs)-1 do y := Lton([op(1..b,dgs)]) ; x := Lton([op(b+1..nops(dgs),dgs)]) ; if (x^3+y^3) mod n = 0 and op(b,dgs) <> 0 then RETURN(true); fi; od: false; end:
%p for n from 10 to 1000 do if isA162465(n) then printf("%d,",n); fi; od: # _R. J. Mathar_, Sep 16 2009
%K nonn,base
%O 1,1
%A _Claudio Meller_, Jul 04 2009
%E Definition rephrased by _R. J. Mathar_, Sep 16 2009