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

0,3

Comments

These numbers have the same decimal and negadecimal representations.

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Negadecimal

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]

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

In other bases: A000695, A037314, A276089.

Sequence in context: A001633 A171120 A092907 * A218556 A043314 A088472

Adjacent sequences: A051019 A051020 A051021 * A051023 A051024 A051025

Keyword

nonn,easy,base

Author

Eric W. Weisstein, Dec 11 1999

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

Status

approved