A193431 -id:A193431 - 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

A136414 Put the natural numbers together without spaces and read them two at a time advancing one space each time.

Original entry on oeis.org

12, 23, 34, 45, 56, 67, 78, 89, 91, 10, 1, 11, 11, 12, 21, 13, 31, 14, 41, 15, 51, 16, 61, 17, 71, 18, 81, 19, 92, 20, 2, 21, 12, 22, 22, 23, 32, 24, 42, 25, 52, 26, 62, 27, 72, 28, 82, 29, 93, 30, 3, 31, 13, 32, 23, 33, 33, 34, 43, 35, 53, 36, 63, 37, 73, 38, 83, 39, 94, 40, 4, 41, 14

Offset: 1

Ben Paul Thurston, Mar 31 2008

a(n) = A162711(n,2) for n>1. - Reinhard Zumkeller, Jul 11 2009

			34 is the third entry because the natural numbers written together look like 1234567891011 and reading them off two at a time produces 12, 23, 34, ...

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

Cf. A001704, A193431, A193492, A193493.

a136414 n = a136414_list !! (n-1)
a136414_list = zipWith (+) (tail a007376_list) $ map (10 *) a007376_list
-- Reinhard Zumkeller, Jul 28 2011

a(n) = 10*A007376(n) + A007376(n+1). - Reinhard Zumkeller, Jul 11 2009

More terms from Reinhard Zumkeller, Jul 11 2009

A193493 Put the natural numbers together without spaces and read them five at a time advancing one space each time.

Original entry on oeis.org

12345, 23456, 34567, 45678, 56789, 67891, 78910, 89101, 91011, 10111, 1112, 11121, 11213, 12131, 21314, 13141, 31415, 14151, 41516, 15161, 51617, 16171, 61718, 17181, 71819, 18192, 81920, 19202, 92021, 20212, 2122, 21222, 12223, 22232, 22324, 23242, 32425

Offset: 1

Reinhard Zumkeller, Jul 28 2011

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

Cf. A136414, A193431, A193492.

a193493 n = a193493_list !! (n-1)
a193493_list = f a007376_list where
   f xs'@(x:xs) = ((foldl (\u v -> 10*u + v) 0) $ take 5 xs') : f xs

nn=40;With[{tbl=Flatten[IntegerDigits/@Range[nn]]},Table[FromDigits[ Take[tbl,{n,n+4}]],{n,nn}]](* Harvey P. Dale, Aug 10 2011 *)

a(n) = Sum (A007376(n+k)*10^(4-k): 0 <= k <= 4).

A193492 Put the natural numbers together without spaces and read them four at a time advancing one space each time.

Original entry on oeis.org

1234, 2345, 3456, 4567, 5678, 6789, 7891, 8910, 9101, 1011, 111, 1112, 1121, 1213, 2131, 1314, 3141, 1415, 4151, 1516, 5161, 1617, 6171, 1718, 7181, 1819, 8192, 1920, 9202, 2021, 212, 2122, 1222, 2223, 2232, 2324, 3242, 2425, 4252, 2526, 5262, 2627, 6272

Offset: 1

Reinhard Zumkeller, Jul 28 2011

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

Cf. A136414, A193431, A193493.

a193492 n = a193492_list !! (n-1)
a193492_list = f a007376_list where
   f xs'@(x:xs) = ((foldl (\u v -> 10*u + v) 0) $ take 4 xs') : f xs

FromDigits/@Partition[Flatten[IntegerDigits/@Range[30]],4,1] (* Harvey P. Dale, Aug 19 2012 *)

a(n) = 10*(10*(10*A007376(n)+A007376(n+1))+A007376(n+2))+A007376(n+3).

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

A136414 Put the natural numbers together without spaces and read them two at a time advancing one space each time.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Formula

Extensions

A193493 Put the natural numbers together without spaces and read them five at a time advancing one space each time.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Formula

A193492 Put the natural numbers together without spaces and read them four at a time advancing one space each time.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Formula