A290948 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}.

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

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(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.

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 A348139 A162530

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