

A067030


Numbers n of the form k + reverse(k) for at least one k.


44



0, 2, 4, 6, 8, 10, 11, 12, 14, 16, 18, 22, 33, 44, 55, 66, 77, 88, 99, 101, 110, 121, 132, 141, 143, 154, 161, 165, 176, 181, 187, 198, 201, 202, 221, 222, 241, 242, 261, 262, 281, 282, 302, 303, 322, 323, 342, 343, 362, 363, 382, 383, 403, 404, 423, 424, 443
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OFFSET

0,2


COMMENTS

From Avik Roy (avik_3.1416(AT)yahoo.co.in), Feb 02 2009: (Start)
Any (k+1) digit number N can be represented as
N = Sum_{i=0...k} (ai*10^i).
Rev(N) = Sum_{i=0...k} (ai*10^(ki)).
N+Rev(N) = Sum_{i=0...k} (ai*(10^i+10^(ki))).
The latter formula can produce all the terms of this sequence, the order of terms is explicitly determined by the order of ai's (repetition of terms might not be avoided). (End)


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for sequences related to Reverse and Add!


EXAMPLE

0 belongs to the sequence since 0 + 0 = 0;
33 belongs to the sequence since 12 + 21 = 33.


MATHEMATICA

M = 10^3; digrev[n_] := IntegerDigits[n] // Reverse // FromDigits; Clear[b]; b[_] = 0; For[n = 1, n <= M, n++, t1 = n + digrev[n]; If[t1 <= M, b[t1] = b[t1] + 1]]; A067030 = Join[{0}, Reap[For[n = 1, n <= M, n++, If[b[n] >= 1, Sow[n]]]][[2, 1]]] (* JeanFrançois Alcover, Oct 01 2016, after N. J. A. Sloane's Maple code in A072040 *)


PROG

(ARIBAS):
function Reverse(n: integer): integer; var i: integer; str, rev: string;
begin str := itoa(n); rev := "";
for i := 0 to length(str)1 do rev := concat(str[i], rev); end;
return atoi(rev); end Reverse;
function A067030(a, b: integer); var k, n: integer;
begin for n := a to b do k := 0; while k <= n do
if n = k+Reverse(k) then write(n, ", "); break; else inc(k); end;
end; end; end A067030;
A067030(0, 500) (* revised May 04 2011 *).
(MAGMA) A067030:=function(a, b); S:=[]; for n in [a..b] do k:=0; while k le n do if n eq k+Seqint(Reverse(Intseq(k))) then Append(~S, n); break; else k+:=1; end if; end while; end for; return S; end function; A067030(0, 500); // May 04 2011


CROSSREFS

Cf. A033865, A067031, A067032, A067033, A067034, A056964.
Sequence in context: A225793 A154809 A153170 * A072427 A050420 A214671
Adjacent sequences: A067027 A067028 A067029 * A067031 A067032 A067033


KEYWORD

base,easy,nonn


AUTHOR

Klaus Brockhaus, Dec 29 2001


STATUS

approved



