A040081 Riesel problem: a(n) = smallest m >= 0 such that n*2^m-1 is prime, or -1 if no such prime exists.

2, 1, 0, 0, 2, 0, 1, 0, 1, 1, 2, 0, 3, 0, 1, 1, 2, 0, 1, 0, 1, 1, 4, 0, 3, 2, 1, 3, 4, 0, 1, 0, 2, 1, 2, 1, 1, 0, 3, 1, 2, 0, 7, 0, 1, 3, 4, 0, 1, 2, 1, 1, 2, 0, 1, 2, 1, 3, 12, 0, 3, 0, 2, 1, 4, 1, 5, 0, 1, 1, 2, 0, 7, 0, 1, 1, 2, 2, 1, 0, 3, 1, 2, 0, 5, 6, 1, 23, 4, 0, 1, 2, 3, 3, 2, 1, 1, 0, 1, 1, 10, 0, 3

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Eric Chen, Table of n, a(n) for n = 1..2292 (first 1000 terms from T. D. Noe)
• Matteo Cati and Dmitrii V. Pasechnik, A database of constructions of Hadamard matrices, arXiv:2411.18897 [math.CO], 2024. See p. 14.
• Hans Riesel, Some large prime numbers. Translated from the Swedish original (Några stora primtal, Elementa 39 (1956), pp. 258-260) by Lars Blomberg.

Crossrefs

Main sequences for Riesel problem: A038699, A040081, A046069, A050412, A052333, A076337, A101036, A108129.

Cf. A010051, A000079.

Programs

Haskell

a040081 = length . takeWhile ((== 0) . a010051) .
                       iterate  ((+ 1) . (* 2)) . (subtract 1)
-- Reinhard Zumkeller, Mar 05 2012

Mathematica

Table[m = 0; While[! PrimeQ[n*2^m - 1], m++]; m, {n, 100}] (* Arkadiusz Wesolowski, Sep 04 2011 *)

PARI

a(n)=for(k=0,2^16,if(ispseudoprime(n*2^k-1), return(k))) \\ Eric Chen, Jun 01 2015

Python

from sympy import isprime
def a(n):
  m = 0
  while not isprime(n*2**m - 1): m += 1
  return m
print([a(n) for n in range(1, 88)]) # Michael S. Branicky, Feb 01 2021