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

1,1

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]

Mathematica

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

Prog

(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

Crossrefs

Cf. A374965; A050412, A052333.

A373799 gives the indices where the primes appear in A374965.

A373804 gives the primes sorted into increasing or5der.

Sequence in context: A095120 A304625 A373804 * A151539 A305555 A323919

Adjacent sequences: A375025 A375026 A375027 * A375029 A375030 A375031

Keyword

nonn

Author

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

Status

approved