A175094 a(1) = 1, a(2) = 3, for n >= 3, a(n) = smallest prime > a(n-1) such that a(n) mod a(n-1) = a(n-2).

1, 3, 7, 17, 41, 181, 1489, 18049, 218077, 1326511, 69196649, 3045979067, 67080736123, 942176284789, 15141901292747, 31225978870283, 577209520957841, 9266578314195739, 575105065001093659, 5760317228325132329, 104260815174853475581, 3967671293872757204407

Offset

1,2

Comments

a(390) has 1001 digits. - Michael S. Branicky, Dec 21 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..389

Mathematica

nmax= 13; a[1]=1; a[2]=3; kmin=1; For[n=3, n<=nmax, n++, For[k=kmin, k>0, k++, If[Mod[Prime[k], a[n-1]]==a[n-2], a[n]=Prime[k]; kmin=k; k=-1]]]; Array[a, nmax] (* Stefano Spezia, Sep 16 2022 *)

Prog

(Python)
from gmpy2 import is_prime
from itertools import count, islice
def agen(): # generator of terms
    c, b = 1, 3
    yield from [c, b]
    for n in count(3):
        a = next(c + b*i for i in count(1) if is_prime(c+b*i))
        c, b = b, a
        yield a
print(list(islice(agen(), 22))) # Michael S. Branicky, Dec 21 2023

Crossrefs

Cf. A175093, A175207, A175208.

Sequence in context: A259855 A058351 A244782 * A086395 A020730 A003440

Adjacent sequences: A175091 A175092 A175093 * A175095 A175096 A175097

Keyword

nonn

Author

Jaroslav Krizek, Jan 31 2010

Extensions

Definition corrected by Stefano Spezia, Sep 16 2022

a(14) and beyond from Michael S. Branicky, Dec 21 2023

Status

approved