A350349 Lexicographically earliest increasing sequence of positive integers such that the Hankel matrix of any odd number of consecutive terms is invertible.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 38, 39, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 80, 81, 82, 83, 85, 86, 87, 88, 90

Offset: 1

Author

Pontus von Brömssen, Dec 26 2021

Keywords

• nonn

Links

• Wikipedia, Hankel matrix

Crossrefs

Cf. A350330, A350348, A350350.

Programs

Python

from sympy import Matrix
from itertools import count
def A350349_list(nmax):
    a=[1]
    for n in range(1,nmax):
        a.append(next(k for k in count(a[-1]+1) if all(Matrix((n-r)//2+1,(n-r)//2+1,lambda i,j:(a[r:]+[k])[i+j]).det()!=0 for r in range(n-2,-1,-2))))
    return a