OFFSET
1,1
COMMENTS
It is conjectured that this sequence is a permutation of the positive integers. If it does not contain all positive integers, then there exists a number of the form q = p*6 - 2, where no solution for j*3 - 1 = A006370^k(q) can be found for any j and any k. Such an example is not yet known.
If the sequence were to contain a positive integer more than once, this would mean that A340407 contains a term of uncountable size, which is not the case.
Let us assume here that this sequence is a permutation, then let a'(m) be the inverse permutation, such that a'(a(n)) = n.
Let p = A006370^k(6*(a(n) + 1) - 2) and choose k such that p is of the form m*6 + 4, then a'((p + 2)/6 - 1) < n.
LINKS
FORMULA
a(1 + Sum_{k=1..n-1} A340407(k)) = 4*n-2.
a(Sum_{k=1..9*n-8} A340407(k)) = 24*n-23.
a(Sum_{k=1..9*n-1} A340407(k)) = 48*n-8.
a(n) = 8*(10^m - 1)/3 + 1 if n = Sum_{k=1..10^m} A340407(k).
a(n) = 4*10^m - 2 if n = -1 + Sum_{k=1..10^m} A340407(k).
a(n) = 4*10^m - 6 if n = -2 + Sum_{k=1..10^m} A340407(k).
a(n) = 5*10^m + (10^(n - 1) - 1)/3 - 13
if n = -3 + Sum_{k=1..10^m} A340407(k).
a(n) = 4*10^m - 10 if n = -4 + Sum_{k=1..10^m} A340407(k).
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Scheuerle, Mar 24 2021
STATUS
approved