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

1,1

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]

Example

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, ...

Prog

(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

Crossrefs

Cf. A090252, A354148, A249033.

Sequence in context: A126324 A035557 A305735 * A248947 A133916 A058589

Adjacent sequences: A354148 A354149 A354150 * A354152 A354153 A354154

Keyword

nonn

Author

N. J. A. Sloane, May 27 2022

Status

approved