A354148 Index of prime(n) in A090252.

2, 3, 4, 6, 8, 9, 10, 12, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 97, 98, 99, 100

Offset: 1

Author

N. J. A. Sloane, May 22 2022

Keywords

• nonn

Comments

All the primes appear in A090252 and in their correct order.

Examples

			A090252 begins 1, 2, 3, 5, 4, 7, 9, ..., so the indices of the primes are 2, 3, 4, 6, ...
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..9800

Crossrefs

Cf. A090252, A354146.

Programs

Python

from math import gcd, prod
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    alst, aset, mink = [1], {1}, 2
    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): yield n
        while mink in aset: mink += 1
print(list(islice(agen(), 83))) # Michael S. Branicky, May 23 2022