A194886 Units' digits of the nonzero decagonal numbers.

1, 0, 7, 2, 5, 6, 5, 2, 7, 0, 1, 0, 7, 2, 5, 6, 5, 2, 7, 0, 1, 0, 7, 2, 5, 6, 5, 2, 7, 0, 1, 0, 7, 2, 5, 6, 5, 2, 7, 0, 1, 0, 7, 2, 5, 6, 5, 2, 7, 0, 1, 0, 7, 2, 5, 6, 5, 2, 7, 0, 1, 0, 7, 2, 5, 6, 5, 2, 7, 0, 1, 0, 7, 2, 5, 6, 5, 2, 7, 0, 1, 0, 7, 2, 5, 6

Offset

1,3

Comments

This is a periodic sequence with period 10 and cycle 1,0,7,2,5,6,5,2,7,0.

Links

Table of n, a(n) for n=1..86.

Formula

a(n) = a(n-10).

a(n) = 35 -a(n-1) -a(n-2) -a(n-3) -a(n-4) -a(n-5) -a(n-6) -a(n-7) -a(n-8) -a(n-9).

a(n) = mod(n(4n-3),10).

G.f.: x*(1 +7*x^2 +2*x^3 +5*x^4 +6*x^5 +5*x^6 +2*x^7 +7*x^8)/((1-x)*(1+x)*(1 +x +x^2 +x^3 +x^4)*(1 -x +x^2 -x^3 +x^4)).

a(n) = -n^2 + 2*n (mod 10). - Arkadiusz Wesolowski, Jul 03 2012

a(n) = A010879(A001107(n)). - Michel Marcus, Aug 10 2015

Example

The seventh nonzero decagonal number is A001107(7)=175, which has units' digit 5. Hence a(7)=5.

Mathematica

Table[Mod[n (4 n - 3), 10], {n, 86}]
PadRight[{}, 120, {1, 0, 7, 2, 5, 6, 5, 2, 7, 0}] (* Harvey P. Dale, Aug 17 2019 *)

Crossrefs

Cf. A001107, A010879.

Sequence in context: A366599 A352890 A066903 * A196764 A074457 A200237

Adjacent sequences: A194883 A194884 A194885 * A194887 A194888 A194889

Keyword

nonn,easy,base

Author

Ant King, Sep 07 2011

Status

approved