Frederick John Bernet III - cp's OEIS frontend

User: Frederick John Bernet III

Frederick John Bernet III has authored 2 sequences.

A327277 Irregular triangle read by rows in which row n lists the first prime(n) primes.

2, 3, 2, 3, 5, 2, 3, 5, 7, 11, 2, 3, 5, 7, 11, 13, 17, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67

Offset: 1

Frederick John Bernet III, Sep 15 2019

			Table begins:
  2, 3;
  2, 3, 5;
  2, 3, 5, 7, 11;
  2, 3, 5, 7, 11, 13, 17;
  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31;
  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41;
  ...

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Right border gives A006450.

A138117 is essentially the same triangle.

m = 8; p = Array[Prime, Prime[m]]; Join @@ (p[[1 ;; p[[#]]]] & /@ Range[m]) (* Amiram Eldar, Sep 24 2019 *)
Table[Take[Prime[Range[Prime[n]]],n],{n,Prime[Range[10]]}]//Flatten (* Harvey P. Dale, Oct 30 2021 *)

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

Original entry on oeis.org

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

Frederick John Bernet III, Sep 06 2019

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

Supersequence of A037308 and A108580.

Cf. A000120, A007953.

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

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

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

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)

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

{ A037308 } union { A108580 }.

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User: Frederick John Bernet III

A327277 Irregular triangle read by rows in which row n lists the first prime(n) primes.

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

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