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A252168 Smallest k>0 such that |(2n-1)-2^k| is prime, or -1 if no such k exists. 2
2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 2, 4, 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, 1, 2, 4, 1, 1, 2, 3, 3, 6, 1, 1, 2, 1, 1, 2, 3, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

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.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A096502, A006285, A133122, A188903.

Cf. A046067, A046069, A067760.

Sequence in context: A086195 A086197 A139336 * A100619 A211984 A275471

Adjacent sequences:  A252165 A252166 A252167 * A252169 A252170 A252171

KEYWORD

nonn,hard

AUTHOR

Eric Chen, Dec 14 2014

STATUS

approved

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)