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

Author

mag(AT)laurel.salles.entpe.fr

Keywords

• nonn
• base
• easy

Comments

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

Examples

			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).
		

Links

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

Crossrefs

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.

Programs

Maple

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

Mathematica

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

PARI

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

Python

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

Formula

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

Extensions

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