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

Author

Frederick John Bernet III, Sep 06 2019

Keywords

• nonn
• base

Links

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

Crossrefs

Supersequence of A037308 and A108580.

Cf. A000120, A007953.

Programs

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 *)

PARI

isok(n) = sumdigits(n, 10) <= sumdigits(n, 2); \\ Michel Marcus, Sep 07 2019

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

Formula

{ A037308 } union { A108580 }.