A300007 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A300007

Index of the inverse/opposite of the n-th 2 X 2 sandpile A300006(n). An involution (self-inverse permutation) of the integers [1..192].

95, 82, 92, 38, 37, 47, 35, 34, 83, 68, 67, 81, 30, 29, 28, 36, 26, 25, 24, 69, 53, 52, 66, 19, 18, 17, 27, 15, 14, 13, 54, 40, 51, 8, 7, 16, 5, 4, 43, 32, 191, 190, 39, 188, 187, 186, 6, 184, 183, 182, 33, 22, 21, 31, 177, 176, 175, 189, 173, 172, 171, 185, 169, 168

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A300006 for the definition of the sandpile addition of 2 X 2 matrices.

A300006(116) = 2222 represents the neutral element e = [2,2;2,2], so a(116) = 116.

A300006 forms a group for the sandpile addition, so for each A300006(n) there exists a unique m, given here as a(n), such that A300006(n) (+) A300006(m) = 2222 (where (+) means the sandpile addition). A300006(m) is also listed as A300008(n).

LINKS

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

EXAMPLE

a(1) = 95 because A300006(1) + A300006(95) = 0112 + 2110 = 2222 represents the unit element of the 2 X 2 sandpile group.

a(2) = 82 because A300006(2) + A300006(82) = 0113 + 2003 = 2116 "topples" to 2222.

PROG

(PARI) A300007(n)=for(m=1, #S2, spa(S2[n], S2[m])==[2, 2; 2, 2]&&return(m)) \\ S2 and spa() being defined as in A300006.

CROSSREFS

Cf. A300006, A300008, A300009.

Sequence in context: A349405 A093007 A033415 * A067266 A171403 A055467

Adjacent sequences: A300004 A300005 A300006 * A300008 A300009 A300010

KEYWORD

nonn,fini,full

AUTHOR

M. F. Hasler, Mar 07 2018

STATUS

approved