A049548 a(n+1) = smallest number not containing any digits of a(n), working in base 4.

0, 1, 2, 3, 4, 10, 12, 21, 32, 53, 128, 213, 512, 853, 2048, 3413, 8192, 13653, 32768, 54613, 131072, 218453, 524288, 873813, 2097152, 3495253, 8388608, 13981013, 33554432, 55924053, 134217728, 223696213, 536870912, 894784853, 2147483648

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4).

Formula

For n>9, a(n)=4*a(n-2) + (a(n-2) mod 4).

a(n) = 5*a(n-2)-4*a(n-4) for n>5; g.f.: x*(32*x^10+16*x^9-12*x^8-12*x^7-17*x^6-x^4-6*x^3-2*x^2+2*x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)). - Colin Barker, Sep 13 2014

Example

Written in base 4 the sequence appears as 0, 1, 2, 3, 10, 22, 30, 111, 200, 311, 2000, 3111, 20000, 31111, 200000, 311111, 2000000, 3111111, etc. So a(9)=311 base 4 =53 base 10.

Mathematica

LinearRecurrence[{0, 5, 0, -4}, {0, 1, 2, 3, 4, 10, 12, 21, 32, 53, 128, 213}, 40] (* Harvey P. Dale, Apr 27 2020 *)

Crossrefs

Cf. A030283, A030439.

Sequence in context: A134170 A276560 A339577 * A005456 A100773 A250112

Adjacent sequences: A049545 A049546 A049547 * A049549 A049550 A049551

Keyword

base,easy,nonn

Author

Henry Bottomley, Dec 28 2000

Status

approved