A338404 Primes p in A158932 such that p = prime(k) = A158932(k) for some k.

2, 3, 397217, 412193, 418927, 421163, 421501, 423763, 426077, 431797, 454859, 456367, 456523, 458993, 475529, 480989, 482393, 484733, 501451, 1003133, 1003469, 1003763, 1003819, 1003931, 1007599, 1007711, 1392851, 1393103, 1393159, 1393187, 1393229, 1393313

Offset: 1

Author

Ya-Ping Lu, Oct 24 2020

Keywords

• nonn

Comments

Sequence A158923, in which every term is the sum of the previous term and the average prime gap, is a "simulation" of the prime number sequence A000040. This sequence lists the terms in A158923 that match those in A000040 both in value and in position, or A158923(m) = A000040(m).

There are 68 matches found for m up to 1073741824 (prime(1073741824)=24563311309), with a(68) = 12496469849.

Crossrefs

Cf. A000040, A158923, A338396.

Programs

PARI

lista(nn) = {my(a = 2); for (n=1, nn, if (a == prime(n), print1(a, ", ")); a += round(log(a)););} \\ Michel Marcus, Oct 31 2020

Python

from sympy import nextprime
from math import log
print(2)
a_last = b_last = m = 2
n = 1
while m >= 2:
    a = a_last + int(log(a_last) + 0.5)
    b = nextprime(b_last)
    if a == b:
        n += 1
        print (m)
    a_last = a
    b_last = b
    m += 1

Formula

a(n) = A158923(m), where m is the n-th index in A158923 such that A158923(m) = A000040(m).