A275512 The consecutive sizes of the blocks of terms containing at least one digit "1" are given by the sequence itself.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 12, 13, 14, 22, 15, 16, 17, 18, 23, 19, 21, 31, 41, 51, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 71, 81, 91, 100, 101, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90

Offset: 1

Author

Eric Angelini, Jul 31 2016

Keywords

• nonn
• base
• less

Comments

The sequence starts with a(1) = 1 and is extended with the smallest integer not yet used that does not lead to a contradiction.

Examples

			The blocks of terms including at least a digit "1" are indicated here by parentheses; the successive block-sizes are 1, 2, 3, 4, 5,... which reproduces the sequence itself: (1),2,3,4,5,6,7,8,9,(10,11),20,(12,13,14),22,(15,16,17,18),23,(19,21,31,41,51),24...
		

Crossrefs

Cf. A011531, A052383.

Programs

Maple

isA011531 := proc(n)
    nops(convert(convert(n,base,10),set) intersect {1}) > 0 ;
    simplify(%) ;
end proc:
A011531_next := proc(n)
    local a;
    for a from n+1 do
        if isA011531(a) then
            return a;
        end if;
    end do:
end proc:
isA052383 := proc(n)
    not isA011531(n) ;
end proc:
A052383_next := proc(n)
    local a;
    for a from n+1 do
        if isA052383(a) then
            return a;
        end if;
    end do:
end proc:
A275512grp1 := proc(a)
    local idx1,n ;
    idx1 := 0 ;
    if isA052383(a) then
        return 0;
    end if;
    for n from 1 do
        if isA011531(A275512(n)) then
            if n =1 then
                idx1 := 1;
            elif isA052383(A275512(n-1)) then
                idx1 := idx1+1 ;
            end if;
        end if;
        if A275512(n) = a then
            return idx1 ;
        end if;
    end do:
end proc:
A275512 := proc(n)
    option remember;
    local a,aprev,prev1,grp1,d,seen,reqlen,npr;
    if n =1 then
        1;
    else
        for a from 2 do
            seen := false;
            for npr from 1 to n-1 do
                if procname(npr) = a then
                    seen := true;
                    break;
                end if;
            end do:
            if not seen then
                aprev := procname(n-1) ;
                if isA052383(aprev) then
                    return a;
                else
                    prev1 := 0 ;
                    for d from 1 to n-1 do
                        if isA011531(procname(n-d)) then
                            prev1 := prev1+1 ;
                        else
                            break;
                        end if;
                    end do:
                    grp1 := A275512grp1(aprev) ;
                    reqlen := procname(grp1) ;
                    if reqlen > prev1 then
                        return A011531_next(aprev) ;
                    elif n-prev1-1 > 0 then
                        return A052383_next(procname(n-prev1-1)) ;
                    else
                        return 2 ;
                    end if;
                end if;
            end if;
        end do;
    end if;
end proc:
seq(A275512(n),n=1..100) ; # R. J. Mathar, Jul 31 2016