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A254375
Digital roots of centered heptagonal numbers (A069099).
2
1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8, 7, 4, 8, 1, 1, 8, 4, 7, 8
OFFSET
1,2
COMMENTS
The sequence is periodic with period 9.
FORMULA
a(n) = A010888(A069099(n)).
a(n) = a(n-9).
G.f.: -x*(x^8+8*x^7+4*x^6+7*x^5+8*x^4+7*x^3+4*x^2+8*x+1) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)).
EXAMPLE
a(3) = 4 because the 3rd centered heptagonal number is 22, the digital root of which is 4.
MATHEMATICA
FixedPoint[Plus @@ IntegerDigits[#] &, #] & /@ FoldList[#1 + #2 &, 1, 7 Range@ 80] (* Michael De Vlieger, Feb 01 2015, after Robert G. Wilson v at A069099 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 8, 4, 7, 8, 7, 4, 8, 1}, 86] (* Ray Chandler, Aug 26 2015 *)
PROG
(PARI) m=9; vector(200, n, (m*n*(n-1)/2)%9+1)
CROSSREFS
Sequence in context: A179260 A254246 A369103 * A359837 A019684 A244210
KEYWORD
nonn,easy,base
AUTHOR
Colin Barker, Jan 29 2015
STATUS
approved