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

Author

M. F. Hasler, Mar 07 2018

Keywords

• nonn
• fini
• full

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

Crossrefs

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

Programs

PARI

a(n)=A300006[A300007(n)]

PARI

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].

Formula

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