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A086458
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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.
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4
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0, 1, 10, 11, 29, 34, 99, 100, 101, 104, 105, 106, 109, 110, 111, 114, 115, 116, 119, 120, 121, 124, 125, 274, 275, 276, 279, 280, 281, 284, 285, 286, 289, 290, 291, 294, 295, 296, 299, 311, 314, 315, 316, 319, 320, 321, 324, 325, 326, 329, 330, 331, 334, 335
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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left$(str$(n), 1) = left$(str$(n^3), 1) AND right$(str$(n), 1) = right$(str$(n^3), 1)
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EXAMPLE
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a(12) = 109 appears in the sequence because 109*109*109 = 1295029.
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MATHEMATICA
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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 *)
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PROG
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(PARI) isok(n) = (n == 0) || ((dn=digits(n)) && (ds=digits(n^3)) && (dn[#dn] == ds[#ds])); \\ Michel Marcus, Mar 19 2015
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CROSSREFS
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Cf. A086457 (similar sequence with squares).
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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