The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A008960

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A008960

Final digit of cubes: n^3 mod 10.
(history; published version)

#59 by Michael De Vlieger at Mon Dec 18 12:16:58 EST 2023

STATUS

proposed

approved

#58 by Michel Marcus at Mon Dec 18 09:29:40 EST 2023

STATUS

editing

proposed

#57 by Michel Marcus at Mon Dec 18 09:29:24 EST 2023

LINKS

<a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

STATUS

proposed

editing

#56 by Paolo P. Lava at Mon Dec 18 09:28:17 EST 2023

STATUS

editing

proposed

#55 by Paolo P. Lava at Mon Dec 18 09:28:15 EST 2023

FORMULA

a(n) = 1/5*(5*(n mod 10)-3*((n+1) mod 10)+((n+2) mod 10)+2*((n+3) mod 10)+2*((n+6) mod 10)+((n+7) mod 10)-3*((n+8) mod 10)). - Paolo P. Lava, Nov 24 2006

STATUS

approved

editing

#54 by Charles R Greathouse IV at Thu Sep 08 08:44:36 EDT 2022

PROG

(MAGMAMagma) [n^3 mod 10: n in [0..80]]; // Vincenzo Librandi, Mar 26 2013

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#53 by N. J. A. Sloane at Sat Dec 07 12:18:17 EST 2019

PROG

(Sage) [power_mod(n, 3, 10 ) for n in xrangerange(0, 81)] # Zerinvary Lajos, Oct 29 2009

Discussion

Sat Dec 07

12:18

OEIS Server: https://oeis.org/edit/global/2837

#52 by Bruno Berselli at Mon Nov 30 11:14:36 EST 2015

STATUS

proposed

approved

#51 by Colin Barker at Mon Nov 30 11:12:31 EST 2015

STATUS

editing

proposed

#50 by Colin Barker at Mon Nov 30 11:11:41 EST 2015

DATA

0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5

FORMULA

G.f.: x*(1+8*x+7*x^2+4*x^3+5*x^4+6*x^5+3*x^6+2*x^7+9*x^8) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)). - Colin Barker, Nov 30 2015

PROG

(PARI) concat(0, Vec(x*(1+8*x+7*x^2+4*x^3+5*x^4+6*x^5+3*x^6+2*x^7+9*x^8) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)) + O(x^100))) \\ Colin Barker, Nov 30 2015

STATUS

approved

editing