A376758 The terms of A376201 consist of runs of successive numbers that increase by 1 at each step: a(n) is one-half of length of the n-th such run.

2, 1, 1, 1, 2, 1, 3, 3, 6, 3, 1, 2, 1, 4, 1, 7, 2, 13, 7, 2, 5, 5, 13, 7, 1, 3, 3, 6, 7, 32, 4, 7, 10, 16, 8, 4, 4, 1

Offset

1,1

Comments

[At present it is only a conjecture that the runs have even length, but the proof should not be difficult.]

Links

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

Example

A376201 begins 1, 2, 3, 4, 11, 12, 27, 28, 59, 60, 123, 124, 125, 126, 255, ...
The runs have lengths 4,2,2,4,... so the present sequence begins 2,1,1,2,...

Prog

(Python)
from itertools import count, islice
from sympy import isprime, nextprime
def A376758_gen(): # generator of terms
    c, a, p, q = 2, 2, 3, 4
    for n in count(3):
        b = min(p, q) if isprime(a) else (p if a == (p<<1) else q)
        if b == n:
            if b == a+1:
                c += 1
            else:
                yield c>>1
                c = 1
        if b == p:
            p = nextprime(p)
        else:
            q += isprime(q+1)+1
        a = b
A376758_list = list(islice(A376758_gen(), 10)) # Chai Wah Wu, Oct 14 2024

Crossrefs

Cf. A376198, A376201.

Sequence in context: A206487 A209062 A167204 * A304750 A104306 A074389

Adjacent sequences: A376755 A376756 A376757 * A376759 A376760 A376761

Keyword

nonn,more

Author

N. J. A. Sloane, Oct 07 2024

Extensions

a(33)-a(35) from Michael S. Branicky, Oct 08 2024

a(36)-a(38) from Michael S. Branicky, Oct 15 2024

Status

approved