cp's OEIS Frontend

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

%I A001703 #54 Dec 07 2019 03:50:34
%S A001703 12,123,234,345,456,567,678,789,8910,91011,101112,111213,121314,
%T A001703 131415,141516,151617,161718,171819,181920,192021,202122,212223,
%U A001703 222324,232425,242526,252627,262728,272829,282930,293031,303132,313233,323334,333435,343536,353637,363738
%N A001703 Decimal concatenation of n, n+1, and n+2.
%C A001703 All terms are divisible by 3. Every third term starting with a(2) is divisible by 9. - _Alonso del Arte_, May 27 2013
%H A001703 T. D. Noe, <a href="/A001703/b001703.txt">Table of n, a(n) for n = 0..1000</a>
%F A001703 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
%e A001703 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).
%p A001703 read(transforms) :
%p A001703 A001703 := proc(n)
%p A001703     digcatL([n,n+1,n+2]) ;
%p A001703 end proc:
%p A001703 seq(A001703(n),n=1..20) ; # _R. J. Mathar_, Mar 29 2017
%p A001703 # Third Maple program:
%p A001703 a:= n-> parse(cat(n, n+1, n+2)):
%p A001703 seq(a(n), n=0..50); # _Alois P. Heinz_, Mar 29 2017
%t A001703 concat3Nums[n_] := FromDigits@ Flatten@ IntegerDigits[{n, n + 1, n + 2}]; Array[concat3Nums, 25] (* _Robert G. Wilson v_ *)
%o A001703 (PARI) a(n)=eval(Str(n,n+1,n+2)) \\ _Charles R Greathouse IV_, Oct 08 2011
%o A001703 (Python) for n in range(100): print(int(str(n)+str(n+1)+str(n+2))) # _David F. Marrs_, Sep 18 2018
%Y A001703 Cf. A074991.
%Y A001703 For concatenations of exactly k consecutive integers see A000027 (k=1), A127421 (k=2), A279204 (k=4). For 2 or more see A035333.
%Y A001703 See also A127422, A127423, A127424.
%K A001703 nonn,base,easy
%O A001703 0,1
%A A001703 mag(AT)laurel.salles.entpe.fr
%E A001703 Initial term 12 added and offset changed to 0 at the suggestion of _R. J. Mathar_. - _N. J. A. Sloane_, Mar 29 2017