A354151 Lengths of successive runs of primes in A090252.

3, 1, 3, 2, 7, 5, 1, 14, 11, 2, 1, 29, 22, 5, 2, 58, 1, 45, 1, 1, 10, 1, 5, 117, 3, 90, 2, 2, 21, 2, 11, 1, 1, 39, 195, 7, 181, 5, 5, 1, 42, 7, 23, 2, 3, 79, 391, 14, 1, 362, 1, 11, 1, 1, 11, 1, 1, 3, 1, 85, 15, 46, 5, 7, 158, 782, 1, 29, 1, 3, 1, 725, 1, 1, 2, 22, 2, 2, 23, 2, 3, 7, 2, 170, 31, 93, 1, 1, 11, 15, 317, 1, 1089, 475, 2, 58, 1, 1, 3, 7, 2, 1450

Offset: 1

Author

N. J. A. Sloane, May 27 2022

Keywords

• nonn

Examples

			A090252 begins 1, 2, 3, 5, 4, 7, 9, 11, 13, 17, 8, 19, 23, 25, 21, 29, 31, ... which, writing N for a nonprime and P for a prime, is NPPPNPNPPPNPPNPP...  The runs of primes have lengths 3, 1, 3, 2, ...
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..2148 [Based on Russ Cox's 5 million term data file for A090252]

Crossrefs

Cf. A090252, A354148, A249033.

Programs

Python

from math import gcd, prod
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    alst, aset, mink, run = [1], {1}, 2, 0
    for n in count(2):
        k, s = mink, n - n//2
        prodall = prod(alst[n-n//2-1:n-1])
        while k in aset or gcd(prodall, k) != 1: k += 1
        alst.append(k); aset.add(k)
        if isprime(k): run += 1
        elif run > 0: yield run; run = 0
        while mink in aset: mink += 1
print(list(islice(agen(), 45))) # Michael S. Branicky, May 28 2022