%I #39 Sep 21 2024 12:39:38

%S 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,

%T 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,

%U 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

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

%H Eric Chen, <a href="/A040081/b040081.txt">Table of n, a(n) for n = 1..2292</a> (first 1000 terms from T. D. Noe)

%H Hans Riesel, <a href="/A076337/a076337.pdf">Some large prime numbers</a>. Translated from the Swedish original (Några stora primtal, Elementa 39 (1956), pp. 258-260) by Lars Blomberg.

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

%o (Haskell)

%o a040081 = length . takeWhile ((== 0) . a010051) .

%o iterate ((+ 1) . (* 2)) . (subtract 1)

%o -- _Reinhard Zumkeller_, Mar 05 2012

%o (PARI) a(n)=for(k=0,2^16,if(ispseudoprime(n*2^k-1), return(k))) \\ _Eric Chen_, Jun 01 2015

%o (Python)

%o from sympy import isprime

%o def a(n):

%o m = 0

%o while not isprime(n*2**m - 1): m += 1

%o return m

%o print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Feb 01 2021

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

%Y Cf. A010051, A000079.

%K nonn,changed

%O 1,1

%A _David W. Wilson_