A325483 Numbers whose sum of their decimal digits is less than or equal to the sum of the digits of their binary representation.

0, 1, 10, 11, 20, 21, 30, 31, 100, 101, 102, 103, 110, 111, 120, 121, 122, 123, 200, 201, 202, 203, 210, 211, 220, 221, 222, 223, 230, 231, 300, 301, 302, 303, 310, 311, 410, 411, 500, 501, 502, 503, 510, 511, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

{ A037308 } union { A108580 }.

Maple

q:= n-> (f-> is(f(n, 10)<=f(n, 2)))((x, b)
          -> add(i, i=convert(x, base, b))):
select(q, [$0..1500])[];  # Alois P. Heinz, Sep 06 2019

Mathematica

Select[Range[0, 1007], Total[IntegerDigits[#]]<=Total[IntegerDigits[#, 2]]&] (* Metin Sariyar, Sep 14 2019 *)

Prog

(Python)
x=0
#Adjust the inequality below to generate more numbers of the sequence
while(x<100):
    x = x+1
    Number = int(bin(x)[2:])
    Bin_Sum = 0
    while(Number > 0):
        Reminder = Number % 10
        Bin_Sum = Bin_Sum + Reminder
        Number = Number //10
    Number = x
    Sum = 0
    while(Number > 0):
        Reminder = Number % 10
        Sum = Sum + Reminder
        Number = Number //10
    if (Sum <= Bin_Sum):
        print(x)
(Python)
def ok(n): return sum(map(int, str(n))) <= bin(n).count('1')
print(list(filter(ok, range(1008)))) # Michael S. Branicky, Oct 11 2021
(PARI) isok(n) = sumdigits(n, 10) <= sumdigits(n, 2); \\ Michel Marcus, Sep 07 2019

Crossrefs

Supersequence of A037308 and A108580.

Cf. A000120, A007953.

Sequence in context: A352339 A197652 A261909 * A235202 A049345 A007623

Adjacent sequences: A325480 A325481 A325482 * A325484 A325485 A325486

Keyword

nonn,base

Author

Frederick John Bernet III, Sep 06 2019

Status

approved