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A050412
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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.
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18
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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
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OFFSET
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1,4
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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If a(n) = k with k>1, then a(2n+1) = k-1. - Robert G. Wilson v, Mar 01 2015
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EXAMPLE
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=if(n<0, 0, s=n; c=1; while(isprime(2*s+1)==0, s=2*s+1; c++); c)
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CROSSREFS
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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
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Robert G. Wilson v, Dec 22 1999
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EXTENSIONS
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More terms from Christian G. Bower, Dec 23 1999
Second definition corrected by Jaroslav Krizek, Feb 13 2011
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STATUS
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approved
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