A127424 -id:A127424 - cp's OEIS frontend

A001703 Decimal concatenation of n, n+1, and n+2.

12, 123, 234, 345, 456, 567, 678, 789, 8910, 91011, 101112, 111213, 121314, 131415, 141516, 151617, 161718, 171819, 181920, 192021, 202122, 212223, 222324, 232425, 242526, 252627, 262728, 272829, 282930, 293031, 303132, 313233, 323334, 333435, 343536, 353637, 363738

Offset: 0

mag(AT)laurel.salles.entpe.fr

All terms are divisible by 3. Every third term starting with a(2) is divisible by 9. - Alonso del Arte, May 27 2013

			a(8) = 8910 since the three consecutive numbers starting with 8 are 8, 9, 10, and these concatenate to 8910. (This is the first term that differs from A193431).

T. D. Noe, Table of n, a(n) for n = 0..1000

Cf. A074991.
For concatenations of exactly k consecutive integers see A000027 (k=1), A127421 (k=2), A279204 (k=4). For 2 or more see A035333.
See also A127422, A127423, A127424.

read(transforms) :
A001703 := proc(n)
    digcatL([n,n+1,n+2]) ;
end proc:
seq(A001703(n),n=1..20) ; # R. J. Mathar, Mar 29 2017
# Third Maple program:
a:= n-> parse(cat(n, n+1, n+2)):
seq(a(n), n=0..50); # Alois P. Heinz, Mar 29 2017

concat3Nums[n_] := FromDigits@ Flatten@ IntegerDigits[{n, n + 1, n + 2}]; Array[concat3Nums, 25] (* Robert G. Wilson v *)

a(n)=eval(Str(n,n+1,n+2)) \\ Charles R Greathouse IV, Oct 08 2011

for n in range(100): print(int(str(n)+str(n+1)+str(n+2))) # David F. Marrs, Sep 18 2018

The portion of the sequence with all three numbers having d digits - i.e., n in 10^(d-1)..10^d-3 - is in arithmetic sequence: a(n) = (10^(2*d)+10^d+1)*n + (10^d+2). - Franklin T. Adams-Watters, Oct 07 2011

Initial term 12 added and offset changed to 0 at the suggestion of R. J. Mathar. - N. J. A. Sloane, Mar 29 2017

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

Original entry on oeis.org

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

Artur Jasinski, Jan 14 2007

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

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

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

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.

[Seqint(Intseq(n+1) cat Intseq(n)): n in [0..50]]; // Bruno Berselli, Mar 25 2015

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

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 *)

for n in range(100): print(int(str(n)+str(n+1))) # David F. Marrs, Sep 17 2018

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

More terms from Joshua Zucker, May 15 2007

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

Original entry on oeis.org

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

Artur Jasinski, Jan 14 2007

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

			a(12) = 1211 because 12 and 11 are two consecutive decreasing numbers.

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

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

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

[Seqint(Intseq(n) cat Intseq(n+1)): n in [0..50]]; // Vincenzo Librandi, Nov 08 2016

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

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 *)

a(n) = if (n==1, 1, eval(Str(n, n-1))); \\ Michel Marcus, Oct 14 2016

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

More terms from Emeric Deutsch, Mar 07 2007

A308527 Numbers that, for some x, are the concatenation of x+2, x+1 and x and are divisible by at least two of x+2, x+1 and x.

Original entry on oeis.org

321, 432, 121110, 171615, 343332, 118117116, 232231230, 334333332, 333433333332, 452245214520, 333343333333332, 333334333333333332, 333333433333333333332, 333333343333333333333332

Offset: 1

J. M. Bergot and Robert Israel, Jun 05 2019

For each d>=1, (10^(3*d)-4)/3+10^(2*d) (the concatenation of x+2, x+1 and x where x = (10^d-4)/3) is in the sequence, being divisible by x+1 and x+3. Thus the sequence is infinite.

It appears that a(n) is of the form (10^(3*d)-4)/3+10^(2*d) for n >= 11. - Chai Wah Wu, Jun 19 2019

			232231230 is the concatenation of 232, 231 and 230, and is divisible by 231 and 230, so it is in the sequence.

Chai Wah Wu, Table of n, a(n) for n = 1..56

Cf. A306643.

Subsequence of A127424.

f:=  proc(x)
  local t1, t2, q, a, b;
  t1:= 10^length(x);
  t2:= t1*10^length(x+1);
  q:= x*(1+t1+t2)+2*t2+t1;
    a:= (q/x)::integer;
  b:= (q/(x+1))::integer;
  if a and b then return q elif not(a) and not(b) then return NULL fi;
  if (q/(x+2))::integer then q else NULL fi
end proc:
map(f, [$1..10^8]);

cp's OEIS Frontend

A001703 Decimal concatenation of n, n+1, and n+2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Python

Scala

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

Scala

Extensions

A308527 Numbers that, for some x, are the concatenation of x+2, x+1 and x and are divisible by at least two of x+2, x+1 and x.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple