A249910 Digital root of A003500(n).

2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4, 2, 4, 5, 7, 5, 4

Offset: 0

Author

Peter M. Chema, Dec 17 2014

Keywords

• nonn
• base

Comments

Periodic with cycle of length 6: {2,4,5,7,5,4}. a(n) may be expressed as the decimal expansion of 246/1001. Sequence is palindromic.

Links

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

Crossrefs

Cf. A010888, A003500.

Programs

Mathematica

LinearRecurrence[{1, 0, -1, 1}, {2, 4, 5, 7}, 102] (* Ray Chandler, Jul 25 2016*)

Formula

a(n) = 4*a(n-1) - a(n-2), reduced to digital root.

a(n) = digital root of (2 + sqrt(3))^n + ( 2 - sqrt(3))^n.

Extensions

More terms from Ray Chandler, Jul 25 2016