A300008 Inverse of the n-th 2 X 2 sandpile A300006(n).

2110, 2003, 2101, 1033, 1032, 1130, 1023, 1022, 2011, 1303, 1302, 2002, 333, 332, 331, 1031, 323, 322, 321, 1310, 1203, 1202, 1301, 233, 232, 231, 330, 223, 222, 221, 1210, 1103, 1201, 133, 132, 230, 123, 122, 1120, 1013, 3332, 3331, 1102, 3323, 3322, 3321, 131, 3313

Offset

1,1

Comments

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.

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.

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

Links

M. F. Hasler, Table of n, a(n) for n = 1..192

Formula

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

Prog

(PARI) a(n)=A300006[A300007(n)]
/*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].

Crossrefs

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

Sequence in context: A373527 A284962 A146895 * A068343 A256518 A046334

Adjacent sequences: A300005 A300006 A300007 * A300009 A300010 A300011

Keyword

nonn,fini,full

Author

M. F. Hasler, Mar 07 2018

Status

approved