Search: a033564 -id:a033564
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A018238
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Add 1 to leading digit and put in front.
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+10
3
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OFFSET
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1,2
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COMMENTS
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The concatenation of first n terms (if n is small) yields a palindrome: 1, 121, 1213121, etc. - Amarnath Murthy, Apr 08 2003
This is not the case from n=10 on: According to the formula in A123121 A082215(10) has an even number of digits, the middle digits being "10". (In a strict sense, e.g. Def. 3 of the first reference there, A082215(9) is the last Zimin word on the alphabet {1,...,9}, though.)
While there is less ambiguity about the definition of A018238(10), it is not clear if A018238(11) should start with "11..." or with "10..." (the largest digit of all subsequent terms being "9"). According to the formula in A123121, a(100) has 3 digits more than a(99), so the first choice seems appropriate and has been adopted for the given PARI code.
However, it corresponds to a modified definition, "a(n) = concatenation of n and all preceding terms". a(3) is the only prime term up to a(14) included. The sequence is (1,0,1,0,1,0,...) (mod 3), at least up to a(20). (End)
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LINKS
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PROG
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(PARI) A018238(n, t="")=for(k=2, n, t=Str(t, k-1, t)); eval(Str(n, t)) \\ M. F. Hasler, May 05 2008
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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1, 121, 1213121, 121312141213121, 1213121412131215121312141213121, 121312141213121512131214121312161213121412131215121312141213121, 1213121412131215121312141213121612131214121312151213121412131217121312141213121512131214121312161213121412131215121312141213121
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OFFSET
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1,2
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COMMENTS
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Also called Zimin words.
a(n) is a palindrome for n<10; it is debatable whether a(n) can be called a Zimin word for n>=10 (see the Comments in A018238). - Danny Rorabaugh, Sep 26 2015
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LINKS
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FORMULA
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The Zimin words are defined here by Z_1 = 1, Z_n = Z_{n-1}nZ_{n-1}. - Dmitry Kamenetsky, Sep 30 2006
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MATHEMATICA
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a = {1}; Do[w = IntegerDigits@ a[[n - 1]]; AppendTo[a, FromDigits@ Join[w, IntegerDigits@ n, w]], {n, 2, 7}]; a (* Michael De Vlieger, Sep 26 2015 *)
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CROSSREFS
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See A001511 for another representation of this sequence of digits.
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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"Palindromes" replaced with "Numbers" in sequence name by Danny Rorabaugh, Sep 26 2015
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STATUS
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approved
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A348466
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a(0)=1; for n >= 0, a(n+1) is the concatenation of a(n) and a(n)-1.
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+10
0
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1, 10, 109, 109108, 109108109107, 109108109107109108109106, 109108109107109108109106109108109107109108109105, 109108109107109108109106109108109107109108109105109108109107109108109106109108109107109108109104
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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Nest[Append[#1, #2*10^IntegerLength[#3] + #3] & @@ {#, #[[-1]], #[[-1]] - 1} &, {1, 10}, 6] (* Michael De Vlieger, Oct 20 2021 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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