A102827 "True already", base 10, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 10 contains floor(a(n)/10) copies of the digit a(n) % 10, with a(0) = 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 133

Offset

0,2

Comments

Conjecture: this sequence in various bases never includes a term divisible by the base.

References

Inspired by discussion of "True so far" from Eric Angelini (A102357).

Links

Table of n, a(n) for n=0..71.

Example

The first 9 values of the sequence written in decimal include no '0's and 1 '1', so the next value cannot be 10 (the count of '0's is not 1) but can be 11.

Maple

A102827aux := proc(n, dig)
    local c, d ;
    c := 0 ;
    for d in convert(n, base, 10) do
        if d = dig then
            c := c+1 ;
        end if;
    end do:
    c ;
end proc:
A102827 := proc(n)
    option remember;
    local a, a10, ad, cum;
    if n < 8 then
        return n+1 ;
    end if;
    for a from 1 do
        a10 := floor(a/10) ;
        ad := a mod 10 ;
        cum := add( A102827aux(procname(i), ad), i=0..n-1) ;
        if cum = a10 then
            return a;
        end if;
    end do:
end proc: # R. J. Mathar, Mar 30 2014

Crossrefs

Cf. A102823-A102830, A102357.

Sequence in context: A072544 A009994 A239016 * A190221 A239215 A055571

Adjacent sequences: A102824 A102825 A102826 * A102828 A102829 A102830

Keyword

nonn,easy,base

Author

Hugo van der Sanden, Feb 26 2005

Status

approved