A371050 Numbers whose ternary representation consists of a run of 1's, then a run of 2's, then a run of 0's.

15, 42, 45, 51, 123, 126, 132, 135, 153, 159, 366, 369, 375, 378, 396, 402, 405, 459, 477, 483, 1095, 1098, 1104, 1107, 1125, 1131, 1134, 1188, 1206, 1212, 1215, 1377, 1431, 1449, 1455, 3282, 3285, 3291, 3294, 3312, 3318, 3321, 3375, 3393, 3399, 3402, 3564

Offset

1,1

Comments

All the numbers are multiples of 3.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..680 (All terms up to 10^8.)

Example

The ternary representations of 15, 42, 45 are 120, 1120, 1200.

Mathematica

Map[#[[1]] &, Select[Map[{#, Map[#[[1]] &, Split[IntegerDigits[#, 3]]] == {1, 2, 0}} &,
Range[0, 4000, 3]], #[[2]] &]]  (* this sequence *)
Map[IntegerString[#, 3] &, %]  (* A371051 *)
(* Peter J. C. Moses, Mar 06 2024 *)
Take[With[{nn=6}, Flatten[Table[FromDigits[Join[PadRight[{}, d1, 1], PadRight[{}, d2, 2], PadRight[{}, d0, 0]], 3], {d1, nn}, {d2, nn}, {d0, nn}]]//Union], 50] (* or *) trrQ[n_]:=With[{sp=Split[IntegerDigits[n, 3]]}, Length[sp]==3&&sp[[1, 1]]==1&&sp[[2, 1]]==2&&sp[[3, 1]]==0]; Select[Range[3, 3600, 3], trrQ] (* Harvey P. Dale, Apr 24 2025 *)

Prog

(Python)
from itertools import count, islice
def A371050_gen(): # generator of terms
    return ((3**b*(3**(l-a)-1>>1)+3**b-1)*3**(a-b) for l in count(3) for a in range(2, l) for b in range(1, a))
A371050_list = list(islice(A371050_gen(), 20)) # Chai Wah Wu, Mar 20 2024

Crossrefs

Cf. A007089, A008585, A371051.

Sequence in context: A024845 A056698 A371108 * A070007 A380217 A325041

Adjacent sequences: A371047 A371048 A371049 * A371051 A371052 A371053

Keyword

nonn,base

Author

Clark Kimberling, Mar 17 2024

Status

approved