A387032 Numbers k with digits different from 0 and 1.

2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 222

Offset

1,1

Comments

A062998 contains numbers like 123, 124, 125,.. which are not in this sequence. - R. J. Mathar, Aug 14 2025

A037344 contains numbers like 2047 and 4095 which are not in this sequence. - R. J. Mathar, Aug 14 2025

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

2 is in the sequence since it does not contain 0 nor 1.
12 is not in the sequence since it has digit 1.

Maple

isA387032 := proc(n)
    local d ;
    for d in convert(n, base, 10) do
        if d <=1 then
            return false;
        end if;
    end do:
    true ;
end proc:
A387032 := proc(n)
    option remember ;
    local a;
    if n = 1 then
        2;
    else
        for a from procname(n-1)+1 do
            if isA387032(a) then
                return a;
            end if;
        end do;
    end if;
end proc:
seq(A387032(n), n=1..200) ; # R. J. Mathar, Aug 14 2025

Mathematica

Select[Range[222], Total@ DigitCount[#, 10, {0, 1}] == 0 &] (* Michael De Vlieger, Aug 13 2025 *)

Prog

(PARI) is(n) = if(n <= 0, return(0)); Set(digits(n))[1] >= 2
(Python)
def ok(n): return {"0", "1"} & set(str(n)) == set()
print([k for k in range(223) if ok(k)]) # Michael S. Branicky, Aug 13 2025
(Python)
def A387032(n):
    m = ((k:=7*n+1).bit_length()-1)//3
    return sum((2+((k-(1<<3*m))//(7<<3*j)&7))*10**j for j in range(m)) # Chai Wah Wu, Aug 13 2025

Crossrefs

Intersection of A052382 and A052383.

Cf. A037344, A172424.

Sequence in context: A305463 A062998 A037344 * A249443 A299690 A318276

Adjacent sequences: A387029 A387030 A387031 * A387033 A387034 A387035

Keyword

nonn,base,easy

Author

David A. Corneth, Aug 13 2025

Status

approved