A046069 -id:A046069 - cp's OEIS frontend

A250205 Riesel problem in base 6: Least k > 0 such that n*6^k-1 is prime, or 0 if no such k exists.

1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 2, 1, 0, 2, 1, 1, 1, 0, 1, 1, 2, 2, 0, 4, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 4, 1, 3, 0, 1, 1, 6, 2, 0, 5, 1, 1, 1, 0, 6, 2, 1, 1, 0, 1, 2, 10, 1, 0, 1, 3, 1, 1, 0, 1, 1, 2, 1, 0, 1, 8, 1, 1, 0, 1, 2, 2, 4, 0, 49, 1, 1, 1, 0, 2, 1, 1, 1, 0, 2, 1, 6, 2, 0, 1, 1, 1, 1, 0, 5, 1, 1, 2, 0, 1, 10, 2, 1

Offset: 1

Eric Chen, Mar 13 2015

nonn

a(5j+1) = 0 except for a(1), since (5j+1)*6^k-1 is always divisible by 5, but there are infinitely many numbers not in the form 5j+1 such that a(n) = 0.
a(n) = 0 for n == 84687 mod 10124569, because then n*6^k-1 is always divisible by at least one of 7, 13, 31, 37, 97. - Robert Israel, Mar 17 2015
Conjecture: if n is not in the form 5j+1 and n < 84687, then a(n) > 0.

Eric Chen, Table of n, a(n) for n = 1..1000
Gary Barnes, Riesel conjectures and proofs

Cf. A040081, A046069, A050412, A108129.

Cf. A250204 (Least k > 0 such that n*6^k+1 is prime).

N:= 1000: # to get a(1) to a(N), using k up to 10000
a[1]:= 1:
for n from 2 to N do
if n mod 5 = 1 then a[n]:= 0
else
    for k from 1 to 10000 do
    if isprime(n*6^k-1) then
       a[n]:= k;
         break
      fi
    od
fi
od:
seq(a[n],n=1..N); # Robert Israel, Mar 17 2015

(* m <= 10000 is sufficient up to n = 1000 *)
a[n_] := For[k = 1, k <= 10000, k++, If[PrimeQ[n*6^k - 1], Return[k]]] /. Null -> 0; Table[a[n], {n, 1, 120}]

a(n) = if(n%5==1 && n>1, 0, for(k = 1, 10000, if(ispseudoprime(n*6^k-1), return(k))))

a(A024898(n)) = 1. - Michel Marcus, Mar 16 2015

A101050 Least k such that prime(n)*2^k-1 is prime, or -1 if no such k exists.

Original entry on oeis.org

1, 0, 2, 1, 2, 3, 2, 1, 4, 4, 1, 1, 2, 7, 4, 2, 12, 3, 5, 2, 7, 1, 2, 4, 1, 10, 3, 10, 9, 8, 25, 2, 2, 1, 4, 5, 1, 3, 4, 2, 8, 3, 226, 3, 2, 1, 1, 3, 2, 1, 4, 4, 11, 6, 4, 2, 8, 1, 5, 2, 11, 2, 1, 26, 3, 6, 1, 1, 18, 3, 4, 4, 1, 7, 1, 2, 20, 5, 10, 3, 4, 7, 2, 3, 1, 6, 112, 9, 10, 7, 2, 12, 5, 46, 1, 2, 8

Offset: 1

Pierre CAMI, Jan 21 2005

nonn

Primes p such that p*2^k-1 is composite for all k are called Riesel numbers. The smallest known Riesel number is the prime 509203. Currently, 2293 is the smallest prime whose status is unknown. For a(120), which corresponds to the prime 659, Dave Linton found the least k is 800516. - T. D. Noe, Aug 04 2005

See A046069

Cf. A046069 (least k such that (2n-1)*2^k-1 is prime).

Table[p=Prime[n]; k=0; While[ !PrimeQ[ -1+p*2^k], k++ ]; k, {n, 119}] (* T. D. Noe, Aug 04 2005 *)

Corrected and extended by T. D. Noe, Aug 04 2005

A252168 Smallest k > 0 such that |(2n-1) - 2^k| is prime, or -1 if no such k exists.

Original entry on oeis.org

2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 4, 1, 2, 4, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 4, 1, 2, 4, 3, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 3, 4, 4, 47, 1, 2, 1, 2, 6, 1, 1, 2, 3, 3, 8, 1, 1, 2, 3, 1, 2, 5, 1, 2, 1, 2, 4

Offset: 1

Eric Chen, Dec 14 2014

It is known that a(254602) = -1, because |509203-2^k| is always divisible by 3, 5, 7, 13, 17, or 241. a(1147) is the first unknown term.
a((A101036(n)+1)/2) = -1, so there are infinitely many n such that a(n) = -1.
a((A133122(n)+1)/2) = A096502((A133122(n)-1)/2).

			a(12) = 2 because 2*12-1 = 23 and that 23-2^1 = 21 is not prime but 23-2^2 = 19 is.
a(69) = 6 because 2*69-1 = 137, |137-2^k| is composite for k = 1, 2, 3, 4, 5 and prime for k = 6.
Even the smallest k can be also very large. For example, a(169) = 791.
a(1147) > 65536.

Jinyuan Wang, Table of n, a(n) for n = 1..1146

Cf. A006285, A096502, A133122, A188903.

Cf. A046067, A046069, A067760.

Table[k = 1; While[!PrimeQ[Abs[(2*n-1) - 2^k]], k++]; k, {n, 1, 1000}]

A252168(n)={ my(k=1); n=2*n-1; while(!ispseudoprime(abs(n-2^k)), k++); k }

a(19) corrected by Jinyuan Wang, Mar 25 2023

A225721 Starting with x = n, the number of iterations of x := 2x - 1 until x is prime, or -1 if no prime exists.

Original entry on oeis.org

-1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 6, 1, 1, 0, 1, 2, 2, 1, 2, 0, 1, 0, 8, 3, 1, 2, 1, 0, 2, 5, 1, 0, 1, 0, 2, 1, 2, 0, 583, 1, 2, 1, 1, 0, 1, 1, 4, 1, 2, 0, 5, 0, 4, 7, 1, 2, 1, 0, 2, 1, 1, 0, 3, 0, 2, 1, 1, 4, 3, 0, 2, 3, 1, 0, 1, 2, 4

Offset: 1

Kevin L. Schwartz and Christian N. K. Anderson, May 13 2013

sign

This appears to be a shifted variant of A040076. - R. J. Mathar, May 28 2013

If n is prime, then a(n) = 0. If the sequence never reaches a prime number (for n = 1) or the prime number has more than 1000 digits, -1 is used instead. There are 22 such numbers for n < 10000.

			For a(20), the trajectory is 20->39->77->153->305->609->1217, a prime number. That required 6 steps, so a(20)=6.

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

Cf. A050921 (primes obtained).
Cf. A040081, A038699, A050412, A052333, A046069 (related to the Riesel problem).
Cf. A000668, A000043, A065341 (Mersenne primes), A000079 (powers of 2).
Cf. A007770 (happy numbers), A031177 (unhappy numbers).
Cf. A037274 (home primes), A037271 (steps), A037272, A037272.

y=as.bigz(rep(0,500)); ys=rep(0,500);
for(i in 1:500) { n=as.bigz(i); k=0;
    while(isprime(n)==0 & ndig(n)<1000 & k<5000) { k=k+1; n=2*n-1 }
    if(ndig(n)>=1000 | k>=5000) { ys[i]=-1; y[i]=-1;
    } else {ys[i]=k; y[i]=n; }
}

cp's OEIS Frontend

A250205 Riesel problem in base 6: Least k > 0 such that n*6^k-1 is prime, or 0 if no such k exists.

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A101050 Least k such that prime(n)*2^k-1 is prime, or -1 if no such k exists.

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A252168 Smallest k > 0 such that |(2n-1) - 2^k| is prime, or -1 if no such k exists.

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A225721 Starting with x = n, the number of iterations of x := 2x - 1 until x is prime, or -1 if no prime exists.

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