A227853 Numbers k such that 4620*k - 1 is a safe prime (A005385).

5, 9, 10, 20, 24, 39, 49, 50, 58, 67, 79, 88, 91, 97, 98, 103, 116, 117, 134, 136, 137, 143, 148, 149, 180, 181, 182, 193, 201, 213, 230, 234, 239, 247, 253, 261, 265, 267, 275, 284, 285, 286, 288, 296, 301, 304, 313, 321, 325, 339, 347

Offset: 1

Author

M. F. Hasler, Oct 31 2013

Keywords

• nonn

Comments

The given expression seems to produce safe primes quite frequently. The numbers 6*(4620*a(n)-1) form a subsequence of A230032.

Note that 4620 = 2^2*3*5*7*11.

Is a(4135..4139) = 59497..59501 the only set of 5 terms with common difference = 1? Checked for all terms up to 10^7. - Zak Seidov, Nov 02 2013

This is common because 4620 = 12*5*7*11 contains several small prime factors, which reduces the possible 12x-1 remainders, forcing all safe primes to be in other 12x-1 remainders mod 4620. Something similar would happen if 4620 were replaced with 12*5*7*13 = 5460. - Mark Andreas, Dec 31 2021

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005385, A230032.

Programs

PARI

{f=4*3*5*7*11; for(k=1,2000,isprime(p=k*f-1)&&isprime(p\2)&&print1(k","))}