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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

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

Cf. A010051, A000079.

Sequence in context: A363806 A335021 A176202 * A066745 A239393 A256637

Adjacent sequences: A040078 A040079 A040080 * A040082 A040083 A040084

Keyword

nonn

Author

David W. Wilson

Status

approved