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A010077 a(n) = sum of digits of a(n-1) + sum of digits of a(n-2); a(0) = 0, a(1) = 1. 15
0, 1, 1, 2, 3, 5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10, 2, 3, 5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10, 2, 3, 5, 8, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The digital sum analog (in base 10) of the Fibonacci recurrence. - Hieronymus Fischer, Jun 27 2007

a(n) and Fib(n)=A000045(n) are congruent modulo 9 which implies that (a(n) mod 9) is equal to (Fib(n) mod 9) = A007887(n). Thus (a(n) mod 9) is periodic with the Pisano period A001175(9)=24. - Hieronymus Fischer, Jun 27 2007

a(n)==A004090(n) modulo 9 (A004090(n)=digital sum of Fib(n)). - Hieronymus Fischer, Jun 27 2007

For general bases p>2, we have the inequality 2<=a(n)<=2p-3 (for n>2). Actually, a(n)<=17=A131319(10) for the base p=10. - Hieronymus Fischer, Jun 27 2007

LINKS

Table of n, a(n) for n=0..74.

Index entries for Colombian or self numbers and related sequences

FORMULA

Periodic from n=3 with period 24. - Franklin T. Adams-Watters, Mar 13 2006

a(n) = A030132(n-4) + A030132(n-3) for n>3. - Reinhard Zumkeller, Jul 04 2007

a(n)=a(n-1)+a(n-2)-9*(floor(a(n-1)/10)+floor(a(n-2)/10)). - Hieronymus Fischer, Jun 27 2007

a(n)=floor(a(n-1)/10)+floor(a(n-2)/10)+(a(n-1)mod 10)+(a(n-2)mod 10). - Hieronymus Fischer, Jun 27 2007

a(n)=A059995(a(n-1))+A059995(a(n-2))+A010879(a(n-1))+A010879(a(n-2)). - Hieronymus Fischer, Jun 27 2007

a(n)=Fib(n)-9*sum{1<k<n, Fib(n-k+1)*floor(a(k)/10)} where Fib(n)=A000045(n). - Hieronymus Fischer, Jun 27 2007

MATHEMATICA

a[0] = 0; a[1] = 1; a[n_] := a[n] = Apply[ Plus, IntegerDigits[ a[n - 1] ]] + Apply[ Plus, IntegerDigits[ a[n - 2] ]]; Table[ a[n], {n, 0, 100} ]

nxt[{a_, b_}]:={b, Total[IntegerDigits[a]]+Total[IntegerDigits[b]]}; NestList[ nxt, {0, 1}, 80][[All, 1]] (* Harvey P. Dale, Apr 15 2018 *)

CROSSREFS

Cf. A007953, A007612, A065076.

Cf. A000045, A010073, A010074, A010075, A010076, A131294, A131295, A131296, A131297, A131318, A131319, A131320.

Sequence in context: A074867 A131297 A267809 * A065076 A069638 A237568

Adjacent sequences:  A010074 A010075 A010076 * A010078 A010079 A010080

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Leonid Broukhis

STATUS

approved

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Last modified November 20 16:53 EST 2018. Contains 317412 sequences. (Running on oeis4.)