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

11, 1221, 123321, 12344321, 1234554321, 123456654321, 12345677654321, 1234567887654321, 123456789987654321, 1234567891001987654321, 12345678910111101987654321, 123456789101112211101987654321, 1234567891011121331211101987654321, 12345678910111213144131211101987654321

Offset

1,1

Comments

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

A palindromic version of A173426.

Has same start as A259937, but A259937 generates non-palindromic terms for n>9.

All terms are multiples of 11 (cf. A349805).

Links

Table of n, a(n) for n=1..14.

Formula

a(n) = concatenate( A007908(n), A138793(n) retaining leading zeros).

Example

For n=10 we concatenate 1,2,3,...,10,01,9,8,...3,2,1 getting 1234567891001987654321.

Maple

with(StringTools);
myReverse := n -> Reverse(convert(n, string));
A349804:=proc(n) local i, L, R;
L:=""; R:="";
for i from n to 1 by -1 do
L:=Join( [convert(i, string), L], "");
R:=Join( [R, myReverse(convert(i, string))], "");
od:
parse(Join([L, R], ""));
end proc; # N. J. A. Sloane, Dec 01 2021
# second Maple program:
a:= n-> (s-> parse(cat(s, seq(s[-i], i=1..length(s)))))(cat("", $1..n)):
seq(a(n), n=1..14); # Alois P. Heinz, Dec 01 2021

Mathematica

Table[d = Flatten[IntegerDigits /@ Range@ n]; FromDigits@ Flatten[{d, Reverse@ d}], {n, 13}] (* Michael De Vlieger, Aug 20 2015 *)

Prog

(Python)
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

Crossrefs

Cf. A002477, A173426, A259937, A261570, A349805.

Sequence in context: A233012 A019524 A274766 * A259937 A078269 A015009

Adjacent sequences: A261135 A261136 A261137 * A261139 A261140 A261141

Keyword

nonn,base

Author

Umut Uludag, Aug 10 2015

Extensions

More than the usual number of terms are shown in order to distinguish this from several similar sequences.

Edited by N. J. A. Sloane, Dec 11 2021

Status

approved