A254374 Digital roots of centered pentagonal numbers (A005891).

1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6, 4, 7, 6, 1, 1, 6, 7, 4, 6

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(A005891(n)).

a(n) = a(n-9).

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

Example

a(3) = 7 because the 3rd centered pentagonal number is 16, the digital root of which is 7.

Mathematica

FixedPoint[Plus @@ IntegerDigits[#] &, #] & /@ Table[(5 n^2 + 5 n + 2)/2, {n, 0, 80}] (* Michael De Vlieger, Feb 01 2015 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 6, 7, 4, 6, 4, 7, 6, 1}, 86] (* Ray Chandler, Aug 26 2015 *)
PadRight[{}, 120, {1, 6, 7, 4, 6, 4, 7, 6, 1}] (* Harvey P. Dale, Aug 23 2017 *)

Prog

(PARI) m=5; vector(200, n, (m*n*(n-1)/2)%9+1)

Crossrefs

Cf. A001844, A005891.

Sequence in context: A258989 A005351 A098882 * A019616 A274209 A275276

Adjacent sequences: A254371 A254372 A254373 * A254375 A254376 A254377

Keyword

nonn,easy,base

Author

Colin Barker, Jan 29 2015

Status

approved