A010075 a(n) = sum of base-8 digits of a(n-1) + sum of base-8 digits of a(n-2).

0, 1, 1, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8

Offset: 0

Author

N. J. A. Sloane, Leonid Broukhis

Keywords

• nonn
• base

Comments

The digital sum analog (in base 8) of the Fibonacci recurrence. - Hieronymus Fischer, Jun 27 2007

a(n) and Fib(n)=A000045(n) are congruent modulo 7 which implies that (a(n) mod 7) is equal to (Fib(n) mod 7). Thus (a(n) mod 7) is periodic with the Pisano period A001175(7)=16. - Hieronymus Fischer, Jun 27 2007

For general bases p>2, the inequality 2<=a(n)<=2p-3 holds for n>2. Actually, a(n)<=11=A131319(8) for the base p=8. - Hieronymus Fischer, Jun 27 2007

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A000045, A010073, A010074, A010076, A010077, A131294, A131295, A131296, A131297, A131318, A131319, A131320.

Programs

Mathematica

nxt[{a_,b_}]:={b,Total[IntegerDigits[a,8]]+Total[IntegerDigits[b,8]]}; NestList[ nxt,{0,1},100][[All,1]] (* or *) PadRight[{0,1,1},100,{7,8,8,2,3,5,8,6,7,13,13,12,11,9,6,8}] (* Harvey P. Dale, Apr 19 2020 *)

Formula

Periodic from n=3 with period 16. - Franklin T. Adams-Watters, Mar 13 2006

From Hieronymus Fischer, Jun 27 2007: (Start)

a(n) = a(n-1)+a(n-2)-7*(floor(a(n-1)/8)+floor(a(n-2)/8)).

a(n) = floor(a(n-1)/8)+floor(a(n-2)/8)+(a(n-1)mod 8)+(a(n-2)mod 8).

a(n) = (a(n-1)+a(n-2)+7*(A010877(a(n-1))+A010877(a(n-2))))/8.

a(n) = Fib(n)-7*sum{1A000045(n). (End)

Extensions

Incorrect comment removed by Michel Marcus, Apr 29 2018