A373347 Positive integers k such that A000120(k) > A001511(k).

3, 5, 7, 9, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99

Offset: 1

Author

Paolo Xausa, Jun 01 2024

Keywords

• nonn
• easy
• base

Comments

Numbers whose binary expansion does not encode for any Schreier set (cf. A371176 and A373345).

All odd numbers > 1 are terms.

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A371176.

Cf. A000120, A001511, A008466, A373345, A373360 (first differences).

Programs

Mathematica

Select[Range[100], DigitSum[#, 2] > IntegerExponent[#, 2] + 1 &]

PARI

isok(k) = hammingweight(k) > valuation(2*k, 2); \\ Michel Marcus, Jun 07 2024

Python

def isa(n): return (n - 1).bit_count() < ((n.bit_count() - 1) << 1)
print([n for n in range(100) if isa(n)])  # Peter Luschny, Jun 07 2024

Formula

a(k) = 2^(n+1) - 1; a(k+1) = 2^(n+1) + 1, where k = A008466(n+1).