A370856 Numbers m such that c(0) <= c(1) <= c(2), where c(k) = number of k's in the ternary representation of m.

2, 5, 7, 8, 11, 15, 17, 19, 21, 23, 25, 26, 35, 44, 47, 50, 51, 52, 53, 59, 61, 65, 68, 69, 70, 71, 73, 75, 76, 77, 79, 80, 98, 104, 106, 107, 116, 128, 132, 134, 140, 142, 143, 146, 150, 152, 154, 155, 156, 158, 159, 160, 161, 176, 178, 179, 184, 185, 187

Offset

1,1

Links

Chris R. Rehmann, Table of n, a(n) for n = 1..10000

Example

The ternary representation of 15 is 120, for which c(0)=1 <= c(1)=1 <= c(2)=1. So 15 is in the sequence.

Maple

c:= (p, i)-> coeff(p, x, i):
q:= n-> (p-> c(p, 0)<=c(p, 1) and c(p, 1)<=c(p, 2))(add(x^i, i=convert(n, base, 3))):
select(q, [$0..187])[];  # Alois P. Heinz, Mar 31 2026

Mathematica

Select[Range[1000], DigitCount[#, 3, 0] <= DigitCount[#, 3, 1] <= DigitCount[#, 3, 2] &]

Prog

(MATLAB) nmax = 1000; n = 1:nmax; for k = 1:nmax, c = arrayfun(@(m) sum(dec2base(k, 3)-'0'==m), 0:2); tf(k) = c(1)<=c(2) && c(2)<=c(3); end, a = n(tf); % Chris R. Rehmann, Oct 12 2025
(PARI) select( {is(n, b=3, r=0, c=Vec(0, b))=while(n, c[1+n%b]++; n\=b); c==vecsort(c, , r)}, [1..99]) \\ Optional args allow to chose a different base b, r=4 yields the "reverse" (cf. A370873), c=[2, 1, 0] gives the "strict order" analog A370853. - M. F. Hasler, Mar 31 2026

Crossrefs

Cf. A007089, A370853, A370854, A370855.

Cf. A370873: analog with reversed inequality; A072601 and A072602: base-2 analogs.

Sequence in context: A286693 A032724 A153308 * A216565 A383030 A285938

Adjacent sequences: A370853 A370854 A370855 * A370857 A370858 A370859

Keyword

nonn,base

Author

Clark Kimberling, Mar 03 2024

Status

approved