A046638 Number of cubic residues mod 10^n, or number of distinct n-digit endings of cubes.

1, 10, 63, 505, 5050, 47899, 466237, 4662370, 46308087, 461504593, 4615045930, 46111077091, 460913873941, 4609138739410, 46086465166623, 460840040641225, 4608400406412250, 46083388790070379, 460830811531341997, 4608308115313419970, 46083004243912737927

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