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

Author

Bobby Jacobs, Aug 14 2017

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A003688, A277605, A291179.

Programs

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.]

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