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A194642 Units' digits of the nonzero heptagonal numbers. 0
1, 7, 8, 4, 5, 1, 2, 8, 9, 5, 6, 2, 3, 9, 0, 6, 7, 3, 4, 0, 1, 7, 8, 4, 5, 1, 2, 8, 9, 5, 6, 2, 3, 9, 0, 6, 7, 3, 4, 0, 1, 7, 8, 4, 5, 1, 2, 8, 9, 5, 6, 2, 3, 9, 0, 6, 7, 3, 4, 0, 1, 7, 8, 4, 5, 1, 2, 8, 9, 5, 6, 2, 3, 9, 0, 6, 7, 3, 4, 0, 1, 7, 8, 4, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This is a periodic sequence with period 20 and cycle 1, 7, 8, 4, 5, 1, 2, 8, 9, 5, 6, 2, 3, 9, 0, 6, 7, 3, 4, 0.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,0,0,0,-1,0,0,0,0,1).
FORMULA
a(n) = a(n-20).
a(n) = a(n-5) -a(n-10) +a(n-15).
a(n) = 45 -a(n-1) -a(n-2) -a(n-3) -a(n-4) -a(n-10) -a(n-11) -a(n-12) -a(n-13) -a(n-14).
a(n) = 90 -a(n-1) -a(n-2) -a(n-3) -... -a(n-17) -a(n-18) -a(n-19).
a(n) = (n*(5*n-3)/2) mod 10.
G.f.: -x*(4*x^13 +3*x^12 +7*x^11 +6*x^10 +5*x^8 -5*x^6 +5*x^4 +4*x^3 +8*x^2 +7*x +1) / ((x -1)*(x^2 +1)*(x^4 +x^3 +x^2 +x +1)*(x^8 -x^6 +x^4 -x^2 +1)). - Colin Barker, Sep 23 2013
a(n) = A010879(A000566(n)). - Michel Marcus, Aug 10 2015
EXAMPLE
The seventh nonzero heptagonal number is A000566(7)=112, which has units' digit 2. Hence a(7)=2.
MATHEMATICA
Table[Mod[n*(5*n-3)/2, 10], {n, 100}]
CROSSREFS
Sequence in context: A330161 A197823 A011243 * A114857 A292823 A256920
KEYWORD
nonn,easy,base
AUTHOR
Ant King, Aug 31 2011
STATUS
approved

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)