cp's OEIS Frontend

A179856 Numbers n such that n^3 can be obtained from n by inserting internal (but not necessarily contiguous) digits.

%I A179856 #35 Feb 08 2015 08:49:07
%S A179856 10,11,29,34,99,100,101,106,109,110,114,119,120,124,125,274,275,276,
%T A179856 279,281,290,296,299,314,315,316,319,320,324,325,329,330,335,336,340,
%U A179856 966,970,975,976,979,986,990,996,999,1000,1001,1004,1005,1006,1010,1020,1021,1024,1025,1034,1049,1051
%N A179856 Numbers n such that n^3 can be obtained from n by inserting internal (but not necessarily contiguous) digits.
%C A179856 This is to A046851 as cubes A000578 are to squares A000290. A subset of A086458 (but note that, i.e., 104^3 = 1124864 starts and ends with the same digits as 104, but lacks an internal "0"). If we require the inserted digits to fill contiguous places, another sequence results, which does not contain 106, for example.
%e A179856 34^3 = 39304 (insert "930" into "34").
%e A179856 106^3 = 1191016 (insert "191" and "1" into "106").
%p A179856 A000030 := proc(n) if n= 0 then 0; else op(-1,convert(n,base,10)) ; end if; end proc:
%p A179856 A010879 := proc(n) n mod 10 ; end proc:
%p A179856 isA086458 := proc(n) A000030(n) = A000030(n^3) and A010879(n) = A010879(n^3) ; end proc:
%p A179856 subsI := proc(c,L) for i from 1 to nops(L) do if op(i,L) = c then return i; end if; end do; return -1 ; end proc:
%p A179856 isSubS := proc(Sub,Sup) if nops(Sub) = 1 then if subsI(op(1,Sub),Sup) > 0 then return true; else return false; end if; elif nops(Sub) = 0 then return true; else f := subsI(op(1,Sub),Sup) ; if f < 0 then return false; else procname( subsop(1=NULL,Sub), [op(f+1..nops(Sup),Sup)] ) ; end if; end if; end proc:
%p A179856 isA179856 := proc(n) if isA086458(n) then dgsn := convert(n,base,10) ; dgsn := op(2..nops(dgsn)-1,dgsn) ; dgsn3 := convert(n^3,base,10) ; dgsn3 := op(2..nops(dgsn3)-1,dgsn3) ; isSubS([dgsn],[dgsn3]) ; else false; end if; end proc:
%p A179856 for n from 10 to 1400 do if isA179856(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Jan 30 2011
%Y A179856 Cf. A000578, A046851, A086458.
%K A179856 nonn,base,easy
%O A179856 1,1
%A A179856 _Jonathan Vos Post_, Jan 28 2011