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

%I A051022 #69 Feb 16 2025 08:32:41
%S A051022 0,1,2,3,4,5,6,7,8,9,100,101,102,103,104,105,106,107,108,109,200,201,
%T A051022 202,203,204,205,206,207,208,209,300,301,302,303,304,305,306,307,308,
%U A051022 309,400,401,402,403,404,405,406,407,408,409,500,501,502,503,504,505
%N A051022 Interpolate 0's between each pair of digits of n.
%C A051022 These numbers have the same decimal and negadecimal representations.
%C A051022 Or fixed points of decimal negadecimal conversion. - _Gerald Hillier_, Apr 23 2015
%H A051022 Reinhard Zumkeller, <a href="/A051022/b051022.txt">Table of n, a(n) for n = 0..10000</a>
%H A051022 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Negadecimal.html">Negadecimal</a>
%F A051022 Sums a_i*100^e_i with 0 <= a_i < 10.
%F A051022 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]
%F A051022 a(n) = A338754(n)/11. - _Kritsada Moomuang_, Oct 20 2019 [Corrected by _Kevin Ryde_, Nov 07 2020]
%e A051022 a(23) = 203.
%e A051022 a(99) = 909.
%e A051022 a(100) = 10000.
%e A051022 a(101) = 10001.
%e A051022 a(111) = 10101.
%p A051022 M:= 3: # to get a(0) to a(10^M-1)
%p A051022 A:= 0:
%p A051022 for d from 1 to M do
%p A051022   A:= seq(seq(a*100+b,b=0..9),a=A);
%p A051022 od:
%p A051022 A; # _Robert Israel_, Apr 23 2015
%t A051022 Table[FromDigits[Riffle[IntegerDigits[n],0]],{n,0,60}] (* _Harvey P. Dale_, Nov 17 2013 *)
%t A051022 ToNegaBases[i_Integer, b_Integer] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[(#1 - Mod[ #1, b])/-b &, i, #1 != 0 &], b]]]];
%t A051022 k = 0; lst = {}; While[k < 1001, If[k == ToNegaBases[k, 10], AppendTo[ lst, k]]; k++]; lst (* _Robert G. Wilson v_, Jun 11 2014 *)
%o A051022 (Haskell)
%o A051022 a051022 n = if n < 10 then n else a051022 n' * 100 + r
%o A051022             where (n', r) = divMod n 10
%o A051022 -- _Reinhard Zumkeller_, Apr 20 2011
%o A051022 (HP 49G calculator)
%o A051022 « "" + SREV 0 9
%o A051022   FOR i i "" + DUP 0 + SREPL DROP
%o A051022   NEXT SREV OBJ->
%o A051022 ». _Gerald Hillier_, Apr 23 2015
%o A051022 (PARI) a(n) = fromdigits(digits(n),100); \\ _Kevin Ryde_, Nov 07 2020
%o A051022 (Python)
%o A051022 def a(n): return int("0".join(str(n)))
%o A051022 print([a(n) for n in range(56)]) # _Michael S. Branicky_, Aug 15 2022
%Y A051022 Cf. A039723, A063010, A092908 (primes), A092909 (on primes), A338754 (*11).
%Y A051022 In other bases: A000695, A037314, A276089.
%K A051022 nonn,easy,base
%O A051022 0,3
%A A051022 _Eric W. Weisstein_, Dec 11 1999
%E A051022 More terms and more precise definition from _Jorge Coveiro_, Apr 15 2004 and _David Wasserman_, Feb 26 2008
%E A051022 Edited by _N. J. A. Sloane_, Sep 14 2008 at the suggestion of _R. J. Mathar_
%E A051022 Offset fixed by _Reinhard Zumkeller_, Apr 20 2012