A266225 Least x>1 such that prime(n)*x+x-1 is a prime, or -1 if no such x exists.

2, 2, 2, 3, 2, 3, 3, 3, 2, 2, 4, 3, 2, 3, 4, 2, 3, 7, 4, 5, 6, 3, 2, 2, 3, 5, 3, 4, 4, 2, 3, 2, 6, 3, 3, 4, 4, 3, 3, 2, 2, 4, 2, 6, 3, 3, 7, 7, 3, 4, 2, 2, 4, 2, 3, 5, 3, 4, 6, 2, 7, 2, 4, 5, 3, 3, 4, 3, 6, 3, 3, 2, 3, 6, 7, 3, 4, 3, 4, 3, 2, 6, 2, 3, 3, 2, 6

Offset

1,1

Comments

Conjecture: a(n) > 1.

Links

Table of n, a(n) for n=1..87.

Example

5*2+2-1=11 is a prime, therefore a(3)=2.
7*2+2-1=15 is not a prime, but 7*3+3-1=23 is a prime, so a(4)=3.

Mathematica

lx[n_]:=Module[{x=2, p=Prime[n]}, While[!PrimeQ[p*x+x-1], x++]; x]; Array[ lx, 90] (* Harvey P. Dale, Jul 18 2020 *)

Prog

(Python)
from sympy import isprime
TOP=1000000
for p in range(2, 777):
    if isprime(p):
        failed = True
        for x in range(2, TOP):
            if isprime(p*x+x-1):
                print str(x)+', ',
                failed = False
                break
        if failed: print '-1, ',
(PARI) a(n) = {my(x = 2); while (!isprime(prime(n)*x+x-1), x++); x; } \\ Michel Marcus, Dec 27 2015; corrected Jun 13 2022

Crossrefs

Cf. A000040, A266224.

Sequence in context: A143299 A239428 A257497 * A248596 A076984 A079085

Adjacent sequences: A266222 A266223 A266224 * A266226 A266227 A266228

Keyword

nonn

Author

Alex Ratushnyak, Dec 24 2015

Status

approved