

A290948


Numbers not in any sequence defined by a recurrence b(n) = 3*b(n1) + b(n2) having initial values b(0), b(1) in {0 ... 9}.


2



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

1,1


LINKS

Table of n, a(n) for n=1..55.


EXAMPLE

99 is not in this sequence because it is in the sequence with the recurrence a(n) = 3*a(n1) + a(n2) 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.


PROG

(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.]


CROSSREFS

Cf. A003688, A277605, A291179.
Sequence in context: A165406 A135603 A044866 * A033828 A162530 A204590
Adjacent sequences: A290945 A290946 A290947 * A290949 A290950 A290951


KEYWORD

nonn


AUTHOR

Bobby Jacobs, Aug 14 2017


EXTENSIONS

Entry revised by M. F. Hasler and N. J. A. Sloane, Nov 24 2018
Definition corrected by N. J. A. Sloane, Jun 16 2021 (changing "a()" to "b()"). This is a list, so it has offset 1.  N. J. A. Sloane, Jun 16 2021


STATUS

approved



