A375028 Primes in A374965 in order of their occurrence.

3, 19, 103, 463, 751, 283, 331, 103423, 313, 2671, 1543, 1783, 3823, 68863, 20287, 733, 757, 407896063, 2083, 1093, 2251, 1153, 2371, 1213, 2467, 41023, 2707, 2803, 1453, 119909605576788675546376149602926591, 98238463, 25903, 3405823, 3590143, 3733, 14983, 7603, 7723, 15607, 65306623, 537343, 69151, 3859801644442622798122887215978426484283282692686288680974641672159756287

Offset: 1

Author

Harvey P. Dale and N. J. A. Sloane_, Jul 28 2024

Keywords

• nonn

Comments

Sequences A050412 and A052333 suggest that it is possible that the present sequence has only finitely many terms. - N. J. A. Sloane, Jul 29 2024

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..289 [This b-file ends with a(289) = 838951. Thanks to the work of _Lucas A. Brown_ (see A050412), we can now say that the next term a(290) is the 102410-digit prime 104917*2^340181 - 1. Of course this is too large to include in a b-file. - _N. J. A. Sloane_, Jul 31 2024]
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Crossrefs

Cf. A374965; A050412, A052333.

A373799 gives the indices where the primes appear in A374965.

A373804 gives the primes sorted into increasing or5der.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,If[!PrimeQ[a],2a+1,Prime[n+1]-1]}; Select[NestList[nxt, {1, 1}, 999][[;; , 2]], PrimeQ]

Python

from itertools import islice
from sympy import isprime, nextprime
def A375028_gen(): # generator of terms
    a, p = 1, 3
    while True:
        if isprime(a):
            yield a
            a = p-1
        else:
            a = (a<<1)+1
        p = nextprime(p)
A375028_list = list(islice(A375028_gen(),30)) # Chai Wah Wu, Jul 29 2024