A029898 Pitoun's sequence: a(n+1) is digital root of a(0) + ... + a(n).

1, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2

Offset: 0

Author

Amela2(AT)aol.com

Keywords

• base
• nonn
• nice
• easy

Comments

If the initial 1 is omitted, this is 2^n mod 9. - N. J. A. Sloane

From Cino Hilliard, Dec 31 2004: (Start)

Except for the initial term, also the digital root of 11^n.

Except for the initial term, also the decimal expansion of 125/1001.

Except for the initial term, also the digital root of 2^n. (End)

Aside from the first term, periodic with period 6. - Charles R Greathouse IV, Nov 29 2011

Examples

			1 + 1 + 2 + 4 + 8 + 7 + 5 = 28 -> 2 + 8 = 10 -> a(7) = 1.
		

Links

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

Crossrefs

Cf. A007612, A010888.

Programs

Mathematica

a[n_] := PowerMod[2, n-1, 9]; a[0] = 1; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Nov 29 2011 *)
Join[{1},LinearRecurrence[{1,0,-1,1},{1,2,4,8},110]] (* or *) Join[{1}, PowerMod[2,Range[110],9]] (* Harvey P. Dale, Nov 24 2014 *)

PARI

a(n)=if(n,[5,1,2,4,8,7][n%6+1],1) \\ Charles R Greathouse IV, Nov 29 2011

Sage

[power_mod(2,n,9)for n in range(0, 105)] # Zerinvary Lajos, Nov 03 2009

Formula

a(n) = digital root of 2^(n-1) in base 10 = 2^(n-1) (mod 9). - Olivier Gérard, Jun 06 2001

For n > 0: a(n+6) = a(n) and a(n) = A007612(n+1) - A007612(n) = A010888(A007612(n)). - Reinhard Zumkeller, Feb 27 2006

a(n) = (9 + cos(n*Pi) - 4*sqrt(3)*sin(n*Pi/3))/2 for n > 0 with a(0)=1. - Wesley Ivan Hurt, Oct 04 2018

From Stefano Spezia, Jun 27 2022: (Start)

O.g.f.: (1 + x^2 + 3*x^3 + 4*x^4)/((1 - x)*(1 + x)*(1 - x + x^2)).

E.g.f.: 5*cosh(x) - 2*sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) + 4*(sinh(x) - 1). (End)

Extensions

More terms from Cino Hilliard, Dec 31 2004