A247700 Numbers which have d digits "d", whenever one of their digits is "d", ordered by largest digit, then by size of the number.

1, 22, 122, 212, 221, 333, 1333, 3133, 3313, 3331, 22333, 23233, 23323, 23332, 32233, 32323, 32332, 33223, 33232, 33322, 122333, 123233, 123323, 123332, 132233, 132323, 132332, 133223, 133232, 133322, 212333, 213233, 213323, 213332

Offset

1,2

Comments

This sequence lists the same terms as A108571, but ordered first by the largest digit in the number, then by size. This way, a truncation to the first 1, 5, 80, 14381,... terms is this very same sequence for bases b=2, 3, 4, 5, ...

Links

Table of n, a(n) for n=1..34.

Example

In base 2, the only number with this property is a(1) = 1.
In base 3, this property is again satisfied by 1, but also by the 4 additional terms 22, 122, 212 and 221. They are listed "as such" (without conversion from base 3 to base 10) as a(2),...,a(5).
In base 4, there are 75 more terms (involving three digits "3"), listed as a(6),...,a(80).

Prog

(PARI) a=[]; for(d=1, 3, n=[10^d\9*d]; for(i=1, #a, t=vector(d+#s=digits(a[i]), j, 10^j)~\10; forvec(v=vector(d, j, [1, #t]), c=0; n=concat(n, vector(#t, j, if(setsearch(v, j), d, s[c++]))*t), 2)); a=concat(a, vecsort(n))); a \\ M. F. Hasler, Sep 25 2014

Crossrefs

Sequence in context: A225308 A043498 A108571 * A105776 A044354 A140057

Adjacent sequences: A247697 A247698 A247699 * A247701 A247702 A247703

Keyword

nonn,base

Author

M. F. Hasler, Sep 22 2014

Status

approved