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A127423
a(1) = 1; for n > 1, a(n) = n concatenated with n - 1.
10
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
OFFSET
1,2
COMMENTS
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
A010051(a(A054211(n))) = 1. - Reinhard Zumkeller, Jun 27 2015
LINKS
EXAMPLE
a(12) = 1211 because 12 and 11 are two consecutive decreasing numbers.
MAPLE
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
MATHEMATICA
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 *)
PROG
(Haskell)
a127423 n = a127423_list !! (n-1)
a127423_list = 1 : map read (zipWith (++) (tail iss) iss) :: [Integer]
where iss = map show [1..]
-- Reinhard Zumkeller, Oct 07 2014
(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
KEYWORD
nonn,base
AUTHOR
Artur Jasinski, Jan 14 2007
EXTENSIONS
More terms from Emeric Deutsch, Mar 07 2007
STATUS
approved