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