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

Author

N. J. A. Sloane, Oct 07 2024

Keywords

• nonn
• more

Comments

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

Examples

			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,...
		

Crossrefs

Cf. A376198, A376201.

Programs

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

Extensions

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

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