A104701 Sum of the largest and least digits of two previous terms: a(n) is a sum of the largest and least digits of a(n-1) and a(n-2).

1, 2, 3, 5, 8, 13, 9, 10, 9, 9, 18, 10, 8, 8, 16, 9, 10, 9, 9, 18, 10, 8, 8, 16

Offset

1,2

Comments

The sequence ends with three types of cycle, depending on seed terms a(1) and a(2): p1={9,10,9,9,18,10,8,8,16}, p2={10,5,5}, p3={10,7,7,14,8,9,17}. (At a(1)=a(2)=0 all terms of the sequence, s00, are zero.)

Denote by smn the sequence starting with a(1)=m, a(2)=n, then some sequences are: s02=0,2,2,4,6,10,6,6,12,7,8,15,p1 s03=0,3,3,6,9,15,p2 s12=1,2,3,5,8,13,p1 s07=0,7,7,14,8,9,17,p3 s27=2,7,9,16,10,6,6,12,7,8,15,p1 s49=4,9,13,10,3,3,6,9,15,p2 s67=6,7,13,8,9,17,p3. From 54 different nontrivial sequences with seeds from 0,1 to 9,9, 35 sequences end with p1, 8 with p2 and 11 with p3.

Links

Table of n, a(n) for n=1..24.

Formula

a(n>2)=Maxdigit[a(n-1), a(n-2)]+Mindigit[a(n-1), a(n-2)], a(1)=1, a(2)=2

Mathematica

nxt[{a_, b_}]:=Module[{d=Flatten[IntegerDigits/@{a, b}]}, {b, Max[d]+ Min[d]}]; Transpose[NestList[nxt, {1, 2}, 10]][[1]] (* Harvey P. Dale, Oct 13 2014 *)

Crossrefs

Sequence in context: A214094 A254032 A214365 * A309782 A300999 A074867

Adjacent sequences: A104698 A104699 A104700 * A104702 A104703 A104704

Keyword

base,nonn

Author

Zak Seidov, Mar 19 2005

Status

approved