A085427 -id:A085427 - cp's OEIS frontend

A085917 Least k such that k*2^n - 1 is a semiprime.

5, 4, 2, 1, 3, 5, 4, 2, 1, 2, 1, 3, 6, 3, 3, 3, 3, 6, 3, 3, 3, 2, 1, 3, 6, 3, 6, 3, 6, 3, 3, 11, 16, 8, 4, 2, 1, 8, 4, 2, 1, 15, 13, 15, 16, 8, 4, 2, 1, 6, 3, 17, 15, 12, 6, 3, 4, 2, 1, 3, 6, 3, 3, 5, 3, 2, 1, 5, 6, 3, 48, 24, 12, 6, 3, 12, 6, 3, 10, 5, 4, 2, 1, 3, 3, 31, 21, 17, 15, 11, 13, 24, 12, 6, 3

Offset: 1

Jason Earls, Aug 16 2003

nonn

The first few values of n such that 509203*2^n - 1 is a semiprime, where k = 509203 (the conjectured smallest Riesel number), are: 3,4,16,34,61,82,124,142,163,171,... Conjecture: there are infinitely many semiprimes of this form.

			a(33)=16 because k*2^33 - 1 is not a semiprime for k=1,2,...15, but 16*2^33 - 1 = 223 * 616318177 is.

Sean A. Irvine, Table of n, a(n) for n = 1..500

Cf. A001358, A085427, A076337, A085245.

A239677 Least numbers k such that k*3^n-1 is prime.

Original entry on oeis.org

1, 2, 2, 8, 4, 6, 2, 2, 16, 8, 6, 2, 16, 10, 4, 14, 8, 18, 6, 2, 18, 6, 2, 20, 18, 6, 2, 38, 30, 10, 16, 20, 18, 6, 2, 60, 20, 10, 10, 40, 58, 48, 16, 12, 4, 32, 90, 30, 10, 8, 130, 62, 26, 10, 6, 2, 30, 10, 32, 18, 6, 2, 74, 28, 46, 18, 6, 2, 30, 10, 46, 80, 94, 52

Offset: 1

Derek Orr, Mar 23 2014

nonn

All the numbers in this sequence, excluding a(1), are even.

			1*3^2-1 = 8 is not prime. 2*3^2-1 = 17 is prime. Thus, a(2) = 2.
1*3^5-1 = 242 is not prime. 2*3^5-1 = 485 is not prime. 3*3^5-1 = 728 is not prime. 4*3^5-1 = 971 is prime. Thus, a(5) = 4.

Cf. A085427.

for(n=1, 100, k=0; while(!isprime(k*3^n-1), k++); print1(k, ", ")) \\ Colin Barker, Mar 24 2014

import sympy
from sympy import isprime
def Pow_3(n):
  for k in range(10**4):
    if isprime(k*(3**n)-1):
      return n
n = 1
while n < 100:
  print(Pow_3(n))
  n += 1

cp's OEIS Frontend

A085917 Least k such that k*2^n - 1 is a semiprime.

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