OFFSET
2,1
COMMENTS
This process terminates only when all nonzero digits are prohibited by the restrictions in place for the next term; as b_n(2) = "10" for all n, the digit 1 is only prohibited for odd numbered terms, and as such a(n) must be even for all n. Similar logic can be applied to the digit 3 to show that for all n>3, a(n) is not divisible by 4.
A375232 is the sequence generated when n=10.
LINKS
Jake Bird, Table of n, a(n) for n = 2..88
EXAMPLE
For n = 5:
b_5(1) = 0; as this contains the digit 0, b_5(2), b_5(3) etc. must also contain a 0
b_5(2) = 10 (= 5 in decimal); must contain a 0 from b_5(1); as this contains the digit 1, b_5(4), b_5(6) etc. must also contain a 1, and all other terms must not contain a 1
b_5(3) = 20; must have 0 but not 1
b_5(4) = 100; must have 0 and 1 but not 2
b_5(5) = 30; must have 0 but not 1 or 2
b_5(6) = 102; must have 0, 1, and 2, but not 3
b_5(7) = 40; must have 0 but not 1, 2, or 3
b_5(8) = 101; must have 0 and 1 but not 2, 3, or 4
b_5(9) = 203; must have 0, 2, and 3, but not 1 or 4
b_5(10) = 110; must have 0 and 1 but not 2, 3, or 4
b_5(11) = ---; must have 0 but not 1, 2, 3, or 4 - the only number that fills this condition is 0, but 0 already appears in the sequence, so the sequence terminates after ten terms, and a(5) = 10
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jake Bird, Sep 12 2024
STATUS
approved