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A127423
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a(1) = 1; for n > 1, a(n) = n concatenated with n - 1.
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9
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1, 21, 32, 43, 54, 65, 76, 87, 98, 109, 1110, 1211, 1312, 1413, 1514, 1615, 1716, 1817, 1918, 2019, 2120, 2221, 2322, 2423, 2524, 2625, 2726, 2827, 2928, 3029, 3130, 3231, 3332, 3433, 3534, 3635, 3736, 3837, 3938, 4039, 4140, 4241, 4342, 4443, 4544, 4645
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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a(1) could also have been defined to be 10. In that case the initial terms would be 10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 1110, 1211, 1312, 1413, 1514, 1615, 1716, 1817, 1918, 2019, 2120, 2221, 2322, 2423, 2524, 2625, 2726, 2827, 2928, 3029, 3130, 3231, 3332, 3433, ... (Comment added in case someone is searching for that sequence.) - N. J. A. Sloane, Aug 11 2018
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LINKS
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EXAMPLE
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a(12) = 1211 because 12 and 11 are two consecutive decreasing numbers.
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MAPLE
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c2:=proc(x, y) local s: s:=proc(m) nops(convert(m, base, 10)) end: x*10^s(y)+y: end: seq(c2(n, n-1), n=1..53); # Emeric Deutsch, Mar 07 2007
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MATHEMATICA
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Join[{1}, nxt[n_] := Module[{idn = IntegerDigits[n + 1], idn1 = IntegerDigits[n]}, FromDigits[Join[idn, idn1]]]; Array[nxt, 70]] (* Vincenzo Librandi, Nov 08 2016 *)
nxt[{n_, a_}] := {n + 1, (n + 1) * 10^IntegerLength[n] + n}; NestList[nxt, {1, 1}, 50][[All, 2]] (* Harvey P. Dale, Jan 04 2019 *)
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PROG
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(Haskell)
a127423 n = a127423_list !! (n-1)
a127423_list = 1 : map read (zipWith (++) (tail iss) iss) :: [Integer]
where iss = map show [1..]
(PARI) a(n) = if (n==1, 1, eval(Str(n, n-1))); \\ Michel Marcus, Oct 14 2016
(Magma) [Seqint(Intseq(n) cat Intseq(n+1)): n in [0..50]]; // Vincenzo Librandi, Nov 08 2016
(Scala) val numerStrs = (1 to 50).map(Integer.toString(_)).toList
val concats = (numerStrs.drop(1)) zip (numerStrs.dropRight(1))
concats.map(x => Integer.parseInt(x._1 + x._2)) // Alonso del Arte, Oct 24 2019
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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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EXTENSIONS
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STATUS
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approved
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