A300008 - OEIS

%I #7 Mar 09 2018 18:57:37

%S 2110,2003,2101,1033,1032,1130,1023,1022,2011,1303,1302,2002,333,332,

%T 331,1031,323,322,321,1310,1203,1202,1301,233,232,231,330,223,222,221,

%U 1210,1103,1201,133,132,230,123,122,1120,1013,3332,3331,1102,3323,3322,3321,131,3313

%N Inverse of the n-th 2 X 2 sandpile A300006(n).

%C As in A300006, a 2 X 2 sandpile [a,b;c,d] is encoded as 4-digit number concat(a,b,c,d), and a leading a = 0 is not displayed.

%C By definition, a(n) (+) A300006(n) = 2222, the neutral element, where the sandpile addition (+) is the regular addition followed by "toppling" of digits (i.e., matrix elements) larger than 3, as described in A300006.

%C Sequence A300007(n) gives the index of a(n) in A300006.

%H M. F. Hasler, <a href="/A300008/b300008.txt">Table of n, a(n) for n = 1..192</a>

%F a(n) = A300006(A300007(n)).

%o (PARI) a(n)=A300006[A300007(n)]

%o /*or*/ a(n,e=[2,2;2,2])=for(i=1,#S2,spa(S2[i],S2[n])==e&&return(A300006[i])) \\ spa() and S2 are defined in A300006; A300006[i] is the decimal encoding of S2[i].

%Y For links, references etc. see the main entry A300006.

%K nonn,fini,full

%O 1,1

%A _M. F. Hasler_, Mar 07 2018