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A038724
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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.
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0
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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
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0,3
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COMMENTS
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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, ..., .
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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f[n_] := Block[{id = IntegerDigits@n}, FromDigits@ Join[ IntegerDigits[ Plus @@ id], Abs[ Most@ id - Rest@ id]]]; Table[ f@n, {n, 0, 67}]
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Daniel Mark Pech (pnpmacknam(AT)uswest.net), May 02 2000
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EXTENSIONS
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Corrected the offset, added one term, several comments and the Mathematica coding Robert G. Wilson v, Sep 12 2009
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STATUS
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approved
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