A086458 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

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

LINKS

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

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

Adjacent sequences: A086455 A086456 A086457 * A086459 A086460 A086461

KEYWORD

base,easy,nonn

AUTHOR

Jeremy Gardiner, Jul 20 2003

STATUS

approved