A254375 Digital roots of centered heptagonal numbers (A069099).

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.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

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

Cf. A001844, A069099.

Sequence in context: A179260 A254246 A369103 * A359837 A019684 A244210

Adjacent sequences: A254372 A254373 A254374 * A254376 A254377 A254378

Keyword

nonn,easy,base

Author

Colin Barker, Jan 29 2015

Status

approved