A375088 Mountain Sequence: Sequence that when expressed as non-overlapping mountains, the n-th term is the height and base of the n-th mountain.

1, 2, 1, 2, 3, 4, 3, 2, 1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 3, 2, 1, 2, 1, 2, 3, 4, 3, 2, 1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 3, 2, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4

Offset: 1

Author

Bryle Morga, Jul 29 2024

Keywords

• nonn
• look

Comments

A mountain with base b and height h is a segment starting with b, then climbs to b+h, and goes back to b. So as an example, (1, 2, 3, 2, 1) is a mountain with base of 1 and height of 2.

All positive integers appear in the sequence infinitely many times.

Examples

			a(1) = 1, so the first non-overlapping mountain is 1, 2, 1 with h = b = 1.
Now, a(2) = 2, so the mountain 2, 3, 4, 3, 2 with b = h = 2 is appended to the sequence, and so on.
		

Links

• Bryle Morga, Table of n, a(n) for n = 1..16384
• Bryle Morga, Visualization of the first 10,000,000 terms.

Programs

Python

from itertools import islice
def mountain(h):
    return list(range(h, 2*h + 1)) + list(range(2*h-1, h-1, -1))
def agen():
    a = [1, 2, 1]
    yield 1
    i = 1
    while 1:
       a += mountain(a[i])
       yield a[i]
       i += 1
print(islice(agen(), 104))

Formula

|a(n+1) - a(n)| = 1.