A055785 a(n) = smallest prime q of form q=-1+(p+1)*10^w, where p is n-th prime, or 0 if there is no such prime.

29, 0, 59, 79, 1199999, 139, 179, 199, 239, 2999, 319999999999999999999999999999, 379, 419, 439, 479, 5399, 599, 619, 679999, 719, 739, 79999, 839, 8999, 97999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Offset

1,1

Comments

Branicky searched n<=10000 to 1000 digits.

a(87) = 45*10^11959-1 (11961 digits). - Sidney Cadot, Jan 06 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..86

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (with "None" if the solution is unknown, with each such value tested to at least 1000 digits).

Example

25th term is 9799...999, i.e., digits of Prime[25]=97 are followed by 90 copies of digit 9.

Prog

(Python)
from sympy import isprime, prime
def a(n, wlimit=1000):
    if n == 2: return 0
    pn, w = str(prime(n)), 1
    while not isprime(int(pn+"9"*w)):
        w += 1
        if w > wlimit: return -1
    return int(pn+"9"*w)
print([a(n) for n in range(1, 26)]) # Michael S. Branicky, May 07 2022

Crossrefs

Sequence in context: A067158 A243001 A092995 * A040847 A040848 A040849

Adjacent sequences: A055782 A055783 A055784 * A055786 A055787 A055788

Keyword

base,nonn

Author

Labos Elemer, Jul 13 2000

Extensions

Revised to handle p=3 by Sean A. Irvine, Apr 05 2022

Status

approved