A051022 Interpolate 0's between each pair of digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 500, 501, 502, 503, 504, 505

Offset: 0

Author

Eric W. Weisstein, Dec 11 1999

Keywords

• nonn
• easy
• base

Comments

These numbers have the same decimal and negadecimal representations.

Or fixed points of decimal negadecimal conversion. - Gerald Hillier, Apr 23 2015

Examples

			a(23) = 203.
a(99) = 909.
a(100) = 10000.
a(101) = 10001.
a(111) = 10101.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Negadecimal

Crossrefs

Cf. A039723, A063010, A092908 (primes), A092909 (on primes), A338754 (*11).

In other bases: A000695, A037314, A276089.

Programs

Haskell

a051022 n = if n < 10 then n else a051022 n' * 100 + r
            where (n', r) = divMod n 10
-- Reinhard Zumkeller, Apr 20 2011
(HP 49G calculator)
« "" + SREV 0 9
  FOR i i "" + DUP 0 + SREPL DROP
  NEXT SREV OBJ->
». Gerald Hillier, Apr 23 2015

Maple

M:= 3: # to get a(0) to a(10^M-1)
A:= 0:
for d from 1 to M do
  A:= seq(seq(a*100+b,b=0..9),a=A);
od:
A; # Robert Israel, Apr 23 2015

Mathematica

Table[FromDigits[Riffle[IntegerDigits[n],0]],{n,0,60}] (* Harvey P. Dale, Nov 17 2013 *)
ToNegaBases[i_Integer, b_Integer] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[(#1 - Mod[ #1, b])/-b &, i, #1 != 0 &], b]]]];
k = 0; lst = {}; While[k < 1001, If[k == ToNegaBases[k, 10], AppendTo[ lst, k]]; k++]; lst (* Robert G. Wilson v, Jun 11 2014 *)

PARI

a(n) = fromdigits(digits(n),100); \\ Kevin Ryde, Nov 07 2020

Python

def a(n): return int("0".join(str(n)))
print([a(n) for n in range(56)]) # Michael S. Branicky, Aug 15 2022

Formula

Sums a_i*100^e_i with 0 <= a_i < 10.

a(n) = n if n < 10, otherwise a(floor(n/10))*100 + n mod 10. - Reinhard Zumkeller, Apr 20 2011 [Corrected by Kevin Ryde, Nov 07 2020]

a(n) = A338754(n)/11. - Kritsada Moomuang, Oct 20 2019 [Corrected by Kevin Ryde, Nov 07 2020]

Extensions

More terms and more precise definition from Jorge Coveiro, Apr 15 2004 and David Wasserman, Feb 26 2008

Edited by N. J. A. Sloane, Sep 14 2008 at the suggestion of R. J. Mathar

Offset fixed by Reinhard Zumkeller, Apr 20 2012