A050412 Riesel problem: start with n; repeatedly double and add 1 until reaching a prime. Sequence gives number of steps to reach a prime or 0 if no prime is ever reached.

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 4, 1, 1, 2, 2, 1, 2, 1, 1, 4, 1, 3, 2, 1, 3, 4, 1, 1, 2, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 7, 24, 1, 3, 4, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 12, 2, 3, 4, 2, 1, 4, 1, 5, 2, 1, 1, 2, 4, 7, 2552, 1, 1, 2, 2, 1, 4, 3, 1, 2, 1, 5, 6, 1, 23, 4, 1, 1, 2, 3, 3, 2, 1, 1, 4, 1, 1

Offset

1,4

Comments

a(n) is the smallest m >= 1 such that (n+1)*2^m - 1 is prime (or 0 if no such prime exists).

It is conjectured that n = 509203 is the smallest Riesel number, i.e., n*2^k -1 is composite for every k>0. - Robert G. Wilson v, Mar 01 2015

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..2291 (first 657 terms from T. D. Noe)

Ray Ballinger and Wilfrid Keller, The Riesel Problem: Definition and Status, Proth Search Page.

Formula

If a(n) = k with k>1, then a(2n+1) = k-1. - Robert G. Wilson v, Mar 01 2015

If a(n) = 0, then a(2n+1) is also 0. Conjecture: If a(n) = 1, then a(2n+1) is not 0. - Jeppe Stig Nielsen, Feb 12 2023 -

Example

For n=4; the smallest m>=1 such that (4+1)*2^m-1 is prime is m=2: 5*2^2-1=19 (prime). - Jaroslav Krizek, Feb 13 2011

Maple

A050412 := proc(n)
    local twox1, k ;
    twox1 := 2*n+1 ;
    k := 1;
    while not isprime(twox1) do
        twox1 := 2*twox1+1 ;
        k := k+1 ;
    end do:
    return k;
end proc: # R. J. Mathar, Jul 23 2015

Mathematica

a[n_] := Block[{s=n, c=1}, While[ ! PrimeQ[2*s+1], s = 2*s+1; c++]; c]; Table[ a[n], {n, 1, 99} ] (* Jean-François Alcover, Feb 06 2012, after Pari *)
a[n_] := Block[{k = 1}, While[ !PrimeQ[2^k (n + 1) - 1], k++]; Array[a, 100] (* Robert G. Wilson v, Feb 14 2015 *)

Prog

(PARI) a(n)=if(n<0, 0, s=n; c=1; while(isprime(2*s+1)==0, s=2*s+1; c++); c)

Crossrefs

Cf. A051914, A052333 (primes reached), A052334, A052339, A052340, A050413, A076337, A078680, A101036.

Cf. A040081 (allows m >= 0).

Sequence in context: A078680 A296072 A326700 * A307017 A220424 A182907

Adjacent sequences: A050409 A050410 A050411 * A050413 A050414 A050415

Keyword

nonn,nice,easy

Author

Robert G. Wilson v, Dec 22 1999

Extensions

More terms from Christian G. Bower, Dec 23 1999

Second definition corrected by Jaroslav Krizek, Feb 13 2011

Status

approved