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