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 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. 17
 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 (list; graph; refs; listen; history; text; internal format)
 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 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, 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

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Last modified June 13 04:49 EDT 2021. Contains 344980 sequences. (Running on oeis4.)