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

0,2

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)

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]]] (* 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 *)

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 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
(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

Crossrefs

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

Sequence in context: A225793 A154809 A153170 * A072427 A337430 A050420

Adjacent sequences: A067027 A067028 A067029 * A067031 A067032 A067033

Keyword

base,easy,nonn

Author

Klaus Brockhaus, Dec 29 2001

Status

approved