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A086458
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.
4
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
OFFSET
0,3
COMMENTS
Intersection of A008854 and A144582. - Michel Marcus, Mar 19 2015
LINKS
FORMULA
left$(str$(n), 1) = left$(str$(n^3), 1) AND right$(str$(n), 1) = right$(str$(n^3), 1)
EXAMPLE
a(12) = 109 appears in the sequence because 109*109*109 = 1295029.
MATHEMATICA
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 *)
PROG
(PARI) isok(n) = (n == 0) || ((dn=digits(n)) && (ds=digits(n^3)) && (dn[#dn] == ds[#ds])); \\ Michel Marcus, Mar 19 2015
CROSSREFS
Cf. A086457 (similar sequence with squares).
Cf. A008854 (initial digit), A144582 (final digit).
Sequence in context: A355631 A056067 A300678 * A179856 A098795 A108580
KEYWORD
base,easy,nonn
AUTHOR
Jeremy Gardiner, Jul 20 2003
STATUS
approved