A267495 Autobiographical numbers in base 7: numbers which are fixed or belong to a cycle under the operator T.

22, 10213223, 10311233, 10313314, 10313315, 10313316, 21322314, 21322315, 21322316, 31123314, 31123315, 31123316, 31331415, 31331416, 31331516, 1031223314, 1031223315, 1031223316, 3122331415, 3122331416, 3122331516, 103142132415, 104122232415, 103142132416, 104122232416, 314213241516, 412223241516, 1011112131415, 1011112131416, 1011112131516, 1011112141516, 1011113141516, 1111213141516, 10414213142516, 10413223241516, 10512223142516, 10512213341516, 101112213141516

Offset

1,1

Comments

The T operator numerically summarizes the frequency of digits 0 through 6 in that order when they occur in a number. The numbers and the frequency are written in base 7.

These are all autobiographical numbers in base 7 which lead to a fixed-point or belong to a cycle.

There are three cycles with length 2 (103142132415 /104122232415, 103142132416/104122232416, 314213241516/412223241516), one cycle with length 3 (10512213341516/10512223142516/10414213142516). 29 numbers are fixed-points.

References

Antonia Münchenbach and Nicole Anton George, "Eine Abwandlung der Conway-Folge", contribution to "Jugend forscht" 2016, 2016

Links

Table of n, a(n) for n=1..38.

Andre Kowacs, Studies on the Pea Pattern Sequence, arXiv:1708.06452 [math.HO], 2017.

Example

10213223 contains one 0, two 1's, three 2's and two 3's, so T(10213223) = 1 0 2 1 3 2 2 3, and this is fixed under T.
103142132415 and 104122232415 belong to the cycle of length 2, so
T(T(103142132415)) = T(1 0 4 1 2 2 2 3 2 4 1 5) = 1 0 3 1 4 2 1 3 2 4 1 5.

Crossrefs

Cf. A047841, A267491, A267492, A267493, A267494, A267495, A267496, A267497, A267498, A267499, A267500, A267502.

Sequence in context: A267498 A267497 A267496 * A267494 A104784 A267493

Adjacent sequences: A267492 A267493 A267494 * A267496 A267497 A267498

Keyword

nonn,base,fini,full

Author

Antonia Münchenbach, Jan 16 2016

Status

approved