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.

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

Author

Jeremy Gardiner, Jul 20 2003

Keywords

• base
• easy
• nonn

Comments

Intersection of A008854 and A144582. - Michel Marcus, Mar 19 2015

Examples

			a(12) = 109 appears in the sequence because 109*109*109 = 1295029.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A086457 (similar sequence with squares).

Cf. A008854 (initial digit), A144582 (final digit).

Programs

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 *)

PARI

isok(n) = (n == 0) || ((dn=digits(n)) && (ds=digits(n^3)) && (dn[#dn] == ds[#ds])); \\ Michel Marcus, Mar 19 2015

Formula

left$(str$(n), 1) = left$(str$(n^3), 1) AND right$(str$(n), 1) = right$(str$(n^3), 1)