A256341 Numbers which have only digits 8 and 9 in base 10.

8, 9, 88, 89, 98, 99, 888, 889, 898, 899, 988, 989, 998, 999, 8888, 8889, 8898, 8899, 8988, 8989, 8998, 8999, 9888, 9889, 9898, 9899, 9988, 9989, 9998, 9999, 88888, 88889, 88898, 88899, 88988, 88989, 88998, 88999, 89888, 89889

Offset: 1

Author

M. F. Hasler, Mar 27 2015

Keywords

• nonn
• base
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..8190
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A007088 (digits 0 & 1), A007931 (digits 1 & 2), A032810 (digits 2 & 3), A032834 (digits 3 & 4), A256290 (digits 4 & 5) - A256292 (digits 6 & 7), A256340 (digits 7 & 8).

Programs

Magma

[n: n in [1..35000] | Set(IntegerToSequence(n, 10)) subset {8, 9}];

Magma

[n: n in [1..100000] | Set(Intseq(n)) subset {8,9}]; // Vincenzo Librandi, Aug 19 2016

Mathematica

Flatten[Table[FromDigits[#,10]&/@Tuples[{8,9},n],{n,5}]]

PARI

A256341(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*8

Python

def a(n): return int(bin(n+1)[3:].replace('0', '8').replace('1', '9'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Aug 09 2021

Formula

a(n) = A007931(n) + A002281(A000523(n+1)) = A256341(n) + A256077(n) etc.