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%I #12 May 14 2023 12:24:54
%S 0,1,10,11,29,34,99,100,101,104,105,106,109,110,111,114,115,116,119,
%T 120,121,124,125,274,275,276,279,280,281,284,285,286,289,290,291,294,
%U 295,296,299,311,314,315,316,319,320,321,324,325,326,329,330,331,334,335
%N Both n and n^3 have the same initial digit and also n and n^3 have the same final digit when expressed in base 10.
%C Intersection of A008854 and A144582. - _Michel Marcus_, Mar 19 2015
%H Harvey P. Dale, <a href="/A086458/b086458.txt">Table of n, a(n) for n = 0..2000</a>
%F left$(str$(n), 1) = left$(str$(n^3), 1) AND right$(str$(n), 1) = right$(str$(n^3), 1)
%e a(12) = 109 appears in the sequence because 109*109*109 = 1295029.
%t sidQ[n_]:=Module[{idn=IntegerDigits[n],i3=IntegerDigits[n^3]},idn[[1]]==i3[[1]]&&idn[[-1]]== i3[[-1]]]; Select[Range[0,400],sidQ] (* _Harvey P. Dale_, May 14 2023 *)
%o (PARI) isok(n) = (n == 0) || ((dn=digits(n)) && (ds=digits(n^3)) && (dn[#dn] == ds[#ds])); \\ _Michel Marcus_, Mar 19 2015
%Y Cf. A086457 (similar sequence with squares).
%Y Cf. A008854 (initial digit), A144582 (final digit).
%K base,easy,nonn
%O 0,3
%A _Jeremy Gardiner_, Jul 20 2003
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