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A046638 Number of cubic residues mod 10^n, or number of distinct n-digit endings of cubes. 2
1, 10, 63, 505, 5050, 47899, 466237, 4662370, 46308087, 461504593, 4615045930, 46111077091, 460913873941, 4609138739410, 46086465166623, 460840040641225, 4608400406412250, 46083388790070379, 460830811531341997, 4608308115313419970, 46083004243912737927 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (10,0,134,-1340,0,-1133,11330,0,1000,-10000).

FORMULA

a(n) = A046530(10^n) = A046630(n)*A046633(n). - R. J. Mathar, Feb 28 2011

a(n) ~ 100/217 * 10^n, so large terms start 460829493.... - Charles R Greathouse IV, Jan 03 2013

G.f.: -(10000*x^9+9000*x^8-5130*x^6-2357*x^5+259*x^3+37*x^2-1) / ((x-1)*(2*x-1)*(5*x-1)*(10*x-1)*(x^2+x+1)*(25*x^2+5*x+1)*(4*x^2+2*x+1)). - Alois P. Heinz, Jan 03 2013

EXAMPLE

a(1)=10 because a cube may end with any digit (10 possible combinations); a(2)=63 because a cube may end with 63 2-digit combinations (including leading zeros).

A cube may end with 63 different 2-digit combinations: 00, 01, 03, 04, 07, 08, 09, 11, 12, 13, 16, 17, 19, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 56, 57, 59, 61, 63, 64, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 81, 83, 84, 87, 88, 89, 91, 92, 93, 96, 97, 99. Numbers ending with 14 say cannot be cubes. See also A075821, A075823. - Zak Seidov, Oct 18 2002

PROG

(PARI) a(n)=(5^(n+2)+30)\31*((4<<n+6)\7) \\ Charles R Greathouse IV, Jan 03 2013

CROSSREFS

Cf. A075821, A075823.

Sequence in context: A298716 A271754 A075755 * A101467 A162473 A138661

Adjacent sequences:  A046635 A046636 A046637 * A046639 A046640 A046641

KEYWORD

nonn,easy,base

AUTHOR

David W. Wilson

EXTENSIONS

Edited by N. J. A. Sloane, Oct 19 2008

STATUS

approved

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Last modified February 25 05:01 EST 2020. Contains 332217 sequences. (Running on oeis4.)