A036013 a(n) = smallest number > 1 such that a(1)a(2)...a(n) - 1 is prime (or 1).

2, 2, 2, 3, 2, 4, 2, 3, 6, 4, 5, 5, 5, 10, 4, 3, 5, 8, 22, 13, 14, 2, 5, 5, 2, 20, 9, 9, 24, 5, 26, 15, 14, 25, 25, 4, 9, 30, 9, 21, 12, 11, 10, 2, 40, 19, 8, 13, 11, 50, 3, 25, 25, 8, 5, 25, 46, 19, 47, 54, 9, 13, 14, 43, 4, 24, 28, 16, 33, 25, 152, 2, 11, 22, 6, 78, 87, 7, 10, 21

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..1600 (terms 1..300 from T. D. Noe)

Mathematica

sng1[{t_, a_}]:=Module[{k=2}, While[CompositeQ[t k-1], k++]; {t*k, k}]; NestList[sng1, {2, 2}, 80][[;; , 2]] (* Harvey P. Dale, May 20 2023 *)

Prog

(Python)
from sympy import isprime
from itertools import count
a, p = [2], 2
for _ in range(100):
    q = next(filter(lambda x:isprime(x*p-1), count(2)))
    p = p*q
    a.append(q)
print(a) # Nicholas Stefan Georgescu, Mar 06 2023

Crossrefs

Cf. A036012, A058000 (corresponding primes).

Sequence in context: A076709 A307774 A110021 * A256587 A249616 A307408

Adjacent sequences: A036010 A036011 A036012 * A036014 A036015 A036016

Keyword

nonn,nice,easy

Author

Russell Easterly

Extensions

More terms from Erich Friedman. More terms from Jud McCranie, Jan 26 2000.

Status

approved