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A127423 a(1) = 1; for n > 1, a(n) = n concatenated with n - 1. 9
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)
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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

CROSSREFS

Cf. A127421-A127424, A001704, A248378, A054211, A010051, A317947.

Sequence in context: A118866 A168005 A118535 * A319477 A035137 A261910

Adjacent sequences:  A127420 A127421 A127422 * A127424 A127425 A127426

KEYWORD

nonn,base

AUTHOR

Artur Jasinski, Jan 14 2007

EXTENSIONS

More terms from Emeric Deutsch, Mar 07 2007

STATUS

approved

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Last modified September 18 11:36 EDT 2020. Contains 337169 sequences. (Running on oeis4.)