OFFSET
0,3
COMMENTS
The number of times f(n)=k is represented is: 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, ..., . As an example 11 is 1 since only 10 -> 11.
Further, the least f(n) to equal k beginning at 0: 10, 1, 31, 933, 1233, 8222, 12214, 10212, 14212, ..., . Examples, f(12) = f(21) = 31, f(252) = f(414) = f(630) = 933, f(147) = f(363) = f(525) = f(741) = 1233, f(1313) = f(2024) = f(2420) = f(3131) = f(4202) = 8222, f(1326) = f(2451) = f(3126) = f(3540) = f(4215) = f(5340) = 12214, f(1324) = f(1342) = f(2431) = f(3124) = f(4213) = f(4231) = f(5320) = 10212, f(1346) = f(2435) = f(2453) = f(3542) = f(4235) = f(5324) = f(5342) = f(6431) = 14212, ..., .
n->f(n) beginning with 10: 10, 11, 20, 22, 40, 44, 80, 88, 160, 756, 1821, 12761, 171515, 2066444, 26260200, 184446220, 3174002402, 23263402242, 301143142022, 2331031232220, 24102132111002, ..., .
EXAMPLE
The ordinal number 128 is represented as "1116" (11_16): where 1+2+8="11"; where the difference between 1 and 2 is "1"; and where the difference between 2 and 8 is "6". Conversely, the term "933" may represent the ordinal number 630: where "9" is the sum of 6+3+0; where "3" is the difference between 6 and 3 [6-3="3"]; and where "3" is the difference between 3 and 0.
MATHEMATICA
f[n_] := Block[{id = IntegerDigits@n}, FromDigits@ Join[ IntegerDigits[ Plus @@ id], Abs[ Most@ id - Rest@ id]]]; Table[ f@n, {n, 0, 67}]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Daniel Mark Pech (pnpmacknam(AT)uswest.net), May 02 2000
EXTENSIONS
Corrected the offset, added one term, several comments and the Mathematica coding Robert G. Wilson v, Sep 12 2009
STATUS
approved