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

1,1

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.

Links

Table of n, a(n) for n=1..32.

Formula

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

Prog

(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
(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

Crossrefs

Cf. A000040, A158923, A338396.

Sequence in context: A328211 A324154 A038537 * A235984 A120313 A216981

Adjacent sequences: A338401 A338402 A338403 * A338405 A338406 A338407

Keyword

nonn

Author

Ya-Ping Lu, Oct 24 2020

Status

approved