A067030 Numbers of the form k + reverse(k) for at least one k.

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

Offset: 0

Author

Klaus Brockhaus, Dec 29 2001

Keywords

• base
• easy
• nonn

Comments

From Avik Roy (avik_3.1416(AT)yahoo.co.in), Feb 02 2009: (Start)

Any (k+1)-digit number m can be represented as

m = Sum_{i=0..k} (ai*10^i).

Reverse(m) = Sum_{i=0..k} (ai*10^(k-i)).

m+Reverse(m) = Sum_{i=0..k} (ai*(10^i+10^(k-i))).

The last 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)

Examples

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

Links

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

Crossrefs

Cf. A033865, A067031, A067032, A067033, A067034, A056964.

Programs

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 by Klaus Brockhaus, 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); // Klaus Brockhaus, May 04 2011

Mathematica

M = 10^3; digrev[n_] := IntegerDigits[n] // Reverse // FromDigits; Clear[b]; b[A067030%20=%20Join%5B%7B0%7D,%20Reap%5BFor%5Bn%20=%201,%20n%20%3C=%20M,%20n++,%20If%5Bb%5Bn%5D%20%3E=%201,%20Sow%5Bn%5D%5D%5D%5D%5B%5B2,%201%5D%5D%5D%20(*%20_Jean-Fran%C3%A7ois%20Alcover">] = 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]]] (* _Jean-François Alcover, Oct 01 2016, after N. J. A. Sloane's Maple code in A072040 *)
max = 1000; l = ConstantArray[0, max]; Do[s = n + IntegerReverse@n; If[s <= max, l[[s]]++], {n, max}]; Flatten@{0, Position[l, ?(# != 0 &)]} (* _Hans Rudolf Widmer, Dec 25 2022 *)

Python

def aupto(lim): return sorted(set(t for t in (k + int(str(k)[::-1]) for k in range(lim+1)) if t <= lim))
print(aupto(443)) # Michael S. Branicky, Dec 25 2022