

A038724


Each term describes the ordinal number of its position in the sequence, by a summation of the numerals in that ordinal number and then by the differences between each contiguous pair of the numerals in the order in which they appear.


0



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 20, 31, 42, 53, 64, 75, 86, 97, 108, 22, 31, 40, 51, 62, 73, 84, 95, 106, 117, 33, 42, 51, 60, 71, 82, 93, 104, 115, 126, 44, 53, 62, 71, 80, 91, 102, 113, 124, 135, 55, 64, 73, 82, 91, 100, 111, 122, 133, 144, 66, 75, 84, 93, 102, 111, 120, 131
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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, ..., .


LINKS

Table of n, a(n) for n=0..67.


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 [63="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

Sequence in context: A247753 A267771 A275513 * A106001 A161390 A096106
Adjacent sequences: A038721 A038722 A038723 * A038725 A038726 A038727


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



