A284294 Numbers using only digits 1 and 9.

1, 9, 11, 19, 91, 99, 111, 119, 191, 199, 911, 919, 991, 999, 1111, 1119, 1191, 1199, 1911, 1919, 1991, 1999, 9111, 9119, 9191, 9199, 9911, 9919, 9991, 9999, 11111, 11119, 11191, 11199, 11911, 11919, 11991, 11999, 19111, 19119, 19191, 19199, 19911, 19919

Offset: 1

Author

Jaroslav Krizek, Mar 25 2017

Keywords

• nonn
• base

Comments

Product of digits of terms is a power of 9; subsequence of A284295.

Prime terms are in A020457.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..16382

Crossrefs

Cf. Numbers using only digits 1 and k for k = 0 and k = 2 - 9: A007088 (k = 0), A007931 (k = 2), A032917 (k = 3), A032822 (k = 4) , A276037 (k = 5), A284293 (k = 6), A276039 (k = 7), A213084 (k = 8), this sequence (k = 9).

Programs

Magma

[n: n in [1..20000] | Set(IntegerToSequence(n, 10)) subset {1, 9}];

Mathematica

Join @@ (FromDigits /@ Tuples[{1,9}, #] & /@ Range[5]) (* Giovanni Resta, Mar 25 2017 *)

Formula

The sum of first 2^n terms is (5*20^n + 38*10^n - 95*2^n + 1420)/171. - Giovanni Resta, Mar 25 2017