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A275512 The consecutive sizes of the blocks of terms containing at least one digit "1" are given by the sequence itself. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..93.

EXAMPLE

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...

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

CROSSREFS

Cf. A011531, A052383.

Sequence in context: A032980 A239217 A130571 * A303948 A275413 A273376

Adjacent sequences:  A275509 A275510 A275511 * A275513 A275514 A275515

KEYWORD

nonn,base,less

AUTHOR

Eric Angelini, Jul 31 2016

STATUS

approved

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)