A256340 Numbers which have only digits 7 and 8 in base 10.

7, 8, 77, 78, 87, 88, 777, 778, 787, 788, 877, 878, 887, 888, 7777, 7778, 7787, 7788, 7877, 7878, 7887, 7888, 8777, 8778, 8787, 8788, 8877, 8878, 8887, 8888, 77777, 77778, 77787, 77788, 77877, 77878, 77887, 77888, 78777, 78778, 78787, 78788, 78877, 78878

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

Programs

Magma

[n: n in [1..35000] | Set(IntegerToSequence(n, 10)) subset {7, 8}];

Magma

[n: n in [1..100000] | Set(Intseq(n)) subset {7,8}]; // Vincenzo Librandi, Aug 19 2016

Mathematica

Flatten[Table[FromDigits[#,10]&/@Tuples[{7,8},n],{n,5}]]

PARI

A256340(n)=vector(#n=binary(n+1)[2..-1],i,10^(#n-i))*n~+10^#n\9*7

Python

def a(n): return int(bin(n+1)[3:].replace('0', '7').replace('1', '8'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jul 08 2021

Formula

a(n) = A007931(n) + A002280(A000523(n+1)) = A256292(n) + A256077(n) etc.