cp's OEIS Frontend

A261138 The concatenation of 123456...n and the reverse of this number.

%I A261138 #30 Dec 12 2021 10:19:54
%S A261138 11,1221,123321,12344321,1234554321,123456654321,12345677654321,
%T A261138 1234567887654321,123456789987654321,1234567891001987654321,
%U A261138 12345678910111101987654321,123456789101112211101987654321,1234567891011121331211101987654321,12345678910111213144131211101987654321
%N A261138 The concatenation of 123456...n and the reverse of this number.
%C A261138 Let R(n) denote the number obtained by formally reversing the digits of n, including any leading zeros that may appear; a(n) is the decimal concatenation of 1,2,...,n,R(n),R(n-1),...,R(3),R(2),R(1). - _N. J. A. Sloane_, Dec 01 2021
%C A261138 A palindromic version of A173426.
%C A261138 Has same start as A259937, but A259937 generates non-palindromic terms for n>9.
%C A261138 All terms are multiples of 11 (cf. A349805).
%F A261138 a(n) = concatenate( A007908(n), A138793(n) retaining leading zeros).
%e A261138 For n=10 we concatenate 1,2,3,...,10,01,9,8,...3,2,1 getting 1234567891001987654321.
%p A261138 with(StringTools);
%p A261138 myReverse := n -> Reverse(convert(n,string));
%p A261138 A349804:=proc(n) local i,L,R;
%p A261138 L:=""; R:="";
%p A261138 for i from n to 1 by -1 do
%p A261138 L:=Join( [convert(i,string), L],"");
%p A261138 R:=Join( [R, myReverse(convert(i,string))],"");
%p A261138 od:
%p A261138 parse(Join([L,R],""));
%p A261138 end proc; # _N. J. A. Sloane_, Dec 01 2021
%p A261138 # second Maple program:
%p A261138 a:= n-> (s-> parse(cat(s, seq(s[-i], i=1..length(s)))))(cat("", $1..n)):
%p A261138 seq(a(n), n=1..14); # _Alois P. Heinz_, Dec 01 2021
%t A261138 Table[d = Flatten[IntegerDigits /@ Range@ n]; FromDigits@ Flatten[{d, Reverse@ d}], {n, 13}] (* _Michael De Vlieger_, Aug 20 2015 *)
%o A261138 (Python)
%o A261138 def A349804(n): return int((lambda x: x+x[::-1])(''.join(str(d) for d in range(1,n+1)))) # _Chai Wah Wu_, Dec 01 2021
%Y A261138 Cf. A002477, A173426, A259937, A261570, A349805.
%K A261138 nonn,base
%O A261138 1,1
%A A261138 _Umut Uludag_, Aug 10 2015
%E A261138 More than the usual number of terms are shown in order to distinguish this from several similar sequences.
%E A261138 Edited by _N. J. A. Sloane_, Dec 11 2021