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A290948
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Numbers not in any sequence defined by a recurrence b(n) = 3*b(n-1) + b(n-2) having initial values b(0), b(1) in {0 ... 9}.
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2
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100, 110, 112, 115, 118, 120, 121, 122, 124, 125, 127, 128, 130, 131, 133, 134, 135, 137, 138, 140, 141, 143, 144, 145, 147, 148, 150, 151, 153, 154, 155, 157, 158, 160, 161, 163, 164, 166, 167, 168, 170, 171, 173, 174, 176, 177, 178, 180, 181, 183, 184, 186, 187, 188, 190
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OFFSET
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1,1
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LINKS
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EXAMPLE
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99 is not in this sequence because it is in the sequence with the recurrence a(n) = 3*a(n-1) + a(n-2) starting with 3 and 0: 3, 0, 3, 9, 30, 99, ....
One may check that 100 is the smallest number not in any recurrent sequence of the form a(n+2) = 3a(n+1) + a(n) with a(0) and a(1) in {0, ..., 9}. Therefore a(1) = 100.
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PROG
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(PARI) list(lim)=if(lim<100, return([0..lim\1])); my(v=List([0..99])); for(t=1, 9, my(x=10*t, y=33*t); while(y<=lim, listput(v, y); [x, y]=[y, x+3*y])); for(m=1, 9, for(n=1, 9, my(x=m+3*n, y=3*x+n); while(y<=lim, listput(v, y); [x, y]=[y, x+3*y]))); Set(v) \\ Charles R Greathouse IV, Aug 14 2017 [This computes the complement.]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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