A284069 Numbers whose smallest decimal digit is 8.

8, 88, 89, 98, 888, 889, 898, 899, 988, 989, 998, 8888, 8889, 8898, 8899, 8988, 8989, 8998, 8999, 9888, 9889, 9898, 9899, 9988, 9989, 9998, 88888, 88889, 88898, 88899, 88988, 88989, 88998, 88999, 89888, 89889, 89898, 89899, 89988, 89989, 89998, 89999, 98888

Offset: 1

Author

Jaroslav Krizek, Mar 24 2017

Keywords

• nonn
• base

Comments

Numbers n such that A054054(n) = 8.

Prime terms are in A020472. - Corrected by Robert Israel, Apr 05 2017

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. Sequences of numbers whose smallest decimal digit is k (for k = 0..9): A011540 (k = 0), A284062 (k = 1), A284063 (k = 2), A284064 (k = 3), A284065 (k = 4), A284066 (k = 5), A284067 (k = 6), A284068 (k = 7), this sequence (k = 8), A002283 (k = 9).

Cf. A020472, A054054.

Programs

Magma

[n: n in [1..100000] | Minimum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 8]

Maple

F:= proc(d) local r; # to get all terms with d digits
r:= 8*(10^d-1)/9;
op(sort(convert(map(t -> r + add(10^(j-1),j=t), combinat:-powerset(d) minus {{$1..d}}),list)))
end proc:
map(F, [$1..5]); # Robert Israel, Apr 05 2017

Mathematica

Flatten@ Table[ Most[ FromDigits /@ Tuples[{8,9}, k]], {k,5}] (* Giovanni Resta, Mar 24 2017 *)

PARI

isok(n) = vecmin(digits(n)) == 8; \\ Michel Marcus, Mar 25 2017

Python

print([n for n in range(8, 10**6) if min(str(n))=='8']) # Indranil Ghosh, Apr 06 2017

Formula

From Robert Israel, Apr 05 2017: (Start)

a(2*j+2^(m+1)-m-3) = 10*a(j+2^m-m-1)+8 for j=1..2^m-1.

a(2*j+2^(m+1)-m-2) = 10*a(j+2^m-m-1)+9 for j=1..2^m-1.

a(2^(m+1)-m-2) = 10^m-2. (End)