A127421 Numbers whose decimal expansion is a concatenation of 2 consecutive increasing nonnegative numbers.

1, 12, 23, 34, 45, 56, 67, 78, 89, 910, 1011, 1112, 1213, 1314, 1415, 1516, 1617, 1718, 1819, 1920, 2021, 2122, 2223, 2324, 2425, 2526, 2627, 2728, 2829, 2930, 3031, 3132, 3233, 3334, 3435, 3536, 3637, 3738, 3839, 3940, 4041, 4142, 4243, 4344, 4445, 4546

Offset

1,2

Comments

Primes in the sequence are in A030458. - Bruno Berselli, Mar 25 2015

a(n) always has an even number of digits unless n is in A103456. - Alonso del Arte, Oct 30 2019

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..25000

Example

a(1) = "0,1" = 1.
a(13) = "12,13" = 1213.

Maple

a:= n-> parse(cat(n-1, n)):
seq(a(n), n=1..55);  # Alois P. Heinz, Jul 05 2018

Mathematica

nMax = 49; digitsList = IntegerDigits[Range[0, nMax]]; Table[FromDigits[Flatten[{digitsList[[n]], digitsList[[n + 1]]}]], {n, nMax - 1}] (* Alonso del Arte, Oct 24 2019 *)
Table[FromDigits[Flatten[IntegerDigits/@{n, n+1}]], {n, 0, 50}] (* Harvey P. Dale, May 16 2020 *)

Prog

(Magma) [Seqint(Intseq(n+1) cat Intseq(n)): n in [0..50]]; // Bruno Berselli, Mar 25 2015
(Python) for n in range(100): print(int(str(n)+str(n+1))) # David F. Marrs, Sep 17 2018
(Scala) val numerStrs = (0 to 49).map(Integer.toString(_)).toList
val concats = (numerStrs.dropRight(1)) zip (numerStrs.drop(1))
concats.map(x => Integer.parseInt(x._1 + x._2)) // Alonso del Arte, Oct 24 2019

Crossrefs

A variant of A001704.

For concatenations of exactly k consecutive integers see A000027 (k = 1), A127421 (k = 2), A001703 (k = 3), A279204 (k = 4). For 2 or more see A035333.

Cf. A030458, A127423, A127424, A127425, A103456.

Sequence in context: A072485 A035333 A001704 * A112131 A233032 A088997

Adjacent sequences: A127418 A127419 A127420 * A127422 A127423 A127424

Keyword

nonn,base,easy

Author

Artur Jasinski, Jan 14 2007

Extensions

More terms from Joshua Zucker, May 15 2007

Status

approved