The Six-Seven Function

Backstory behind the “67” meme

It was 2025 when the “67” meme became big. I don’t even know how it went viral, it’s just a number anyways.

“67” Sequence

OEIS A010723 is just 6 and 7 being repeated. Just like the meme

n:    0 1 2 3 4 5 6 ...
a(n): 6 7 6 7 6 7 6 ...

Paolo P. Lava’s Closed Form (2006)

\[a(n) = -\frac{1}{2}(-1)^n + \frac{13}{2}\]

Here is how it’s written in Python:

def six_seven(n):
    return -(1/2) * (-1)**n + 13/2

for n in range(12):
    print(f"a({n}) = {int(six_seven(n))}")

a(0) = 6
a(1) = 7
a(2) = 6
a(3) = 7
a(4) = 6
a(5) = 7
a(6) = 6
a(7) = 7
a(8) = 6
a(9) = 7
a(10) = 6
a(11) = 7

When n is even, (-1)^n = +1, so -(1/2) + 13/2 = 12/2 = 6 When n is odd, (-1)^n = -1, so -(1/2) + 13/2 = 14/2 = 7

A010723

Truly a goated sequence.