A362531 The smallest integer m such that m mod 2k >= k for k = 1, 2, 3, ..., n.

1, 3, 3, 15, 15, 47, 95, 95, 287, 335, 1199, 1199, 1295, 2015, 2879, 2879, 2879, 2879, 2879, 2879, 2879, 43199, 211679, 211679, 211679, 211679, 211679, 211679, 211679, 211679, 3084479, 3084479, 3084479, 3084479, 3084479, 3084479, 302702399, 469909439

Offset

1,2

Comments

Take the square array A(k, l) with k= 1, 2, ... and l = 0, 1, ... such that for each k, A(k, l) takes k zeros and then k ones alternately:

0, 1, 0, 1, 0, 1, 0, 1, ...

0, 0, 1, 1, 0, 0, 1, 1, ...

0, 0, 0, 1, 1, 1, 0, 0, ...

...

Then the a(n)-th column is the first column which begins with n ones.

Links

Table of n, a(n) for n=1..38.

Tomohiro Yamada, Fast Python program, the original program written by nazratt2.

Example

a(3) = 3 since 3 mod 2 = 1, 3 mod 4 = 3 >= 2, 3 mod 6 = 3 (but 3 mod 8 = 3 < 4) while 1 mod 4 = 1 < 2, 2 mod 2 = 0 < 1.

Prog

(PARI) a(n)={my(m); m=1; while(vecmin(vector(n, j, (m%(2*j))/j))<1, m=m+1); m}
(PARI) n=1; for(m=1, 10^9, while(vecmin(vector(n, j, (m%(2*j))/j))>=1, print(n, " ", m); n=n+1))
(Python)
def A362531(n):
    m = 1
    while True:
        for k in range(n, 0, -1):
            if (l:=k-m%(k<<1))>0:
                break
        else:
            return m
        m += l # Chai Wah Wu, Jun 21 2023

Crossrefs

Cf. A053664.

Sequence in context: A172087 A086116 A100735 * A129356 A290344 A217858

Adjacent sequences: A362528 A362529 A362530 * A362532 A362533 A362534

Keyword

nonn

Author

Tomohiro Yamada, Apr 24 2023

Extensions

a(37)-a(38) from Yifan Xie, Apr 24 2023

Status

approved