

A127421


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


9



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
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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


FORMULA

a(n) = n*10^(1 + floor(log(n+1))) + n + 1, with n >= 0.  Paolo P. Lava, May 09 2008


EXAMPLE

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


MAPLE

a:= n> parse(cat(n1, 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 *)


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



