A256290 Numbers which have only digits 4 and 5 in base 10.

4, 5, 44, 45, 54, 55, 444, 445, 454, 455, 544, 545, 554, 555, 4444, 4445, 4454, 4455, 4544, 4545, 4554, 4555, 5444, 5445, 5454, 5455, 5544, 5545, 5554, 5555, 44444, 44445, 44454, 44455, 44544, 44545, 44554, 44555, 45444, 45445, 45454, 45455, 45544

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), A256291 (digits 5 & 6), A256292 (digits 6 & 7), A256340 (digits 7 & 8), A256341 (digits 8 & 9).

Programs

Magma

[n: n in [1..60000] | Set(IntegerToSequence(n, 10)) subset {5, 4}];

Magma

[n: n in [1..100000] | Set(Intseq(n)) subset {4,5}]; // Vincenzo Librandi, Aug 19 2016

Mathematica

Flatten[Table[FromDigits[#,10]&/@Tuples[{4,5},n],{n,5}]]

PARI

A256290(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*4

Python

def A256290(n): return int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1<<2)//9 # Chai Wah Wu, Jul 15 2023

Formula

a(n) = A007931(n) + A002277(A000523(n+1)) = A032834(n) + A256077(n) etc.