A119591 - OEIS

A119591

Least k such that 2*n^k - 1 is prime.

1, 1, 1, 4, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 2, 2, 1, 10, 1, 1, 6, 1, 2, 6, 1, 2, 136, 1, 1, 6, 6, 1, 6, 1, 1, 2, 2, 1, 2, 1, 2, 4, 1, 2, 4, 4, 1, 2, 1, 1, 44, 1, 1, 2, 1, 3, 2, 5, 3, 2, 2, 1, 4, 1, 768, 4, 1, 1, 52, 34, 2, 132, 1, 1, 14, 7, 1, 2, 2, 1, 8, 1, 2, 10, 1, 24, 60, 1, 1, 2, 3, 5, 2, 1, 1, 2, 1, 1

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OFFSET

2,4

COMMENTS

From Eric Chen, Jun 01 2015: (Start)

Conjecture: a(n) is defined for all n.

a(303) > 10000, a(304)..a(360) = {1, 2, 11, 1, 990, 1, 1, 2, 2, 4, 74, 5, 1, 10, 6, 6, 4, 1, 1, 2, 1, 9, 12, 1, 80, 2, 1, 1, 2, 14, 3, 2, 3, 1, 12, 1, 60, 36, 1, 8, 4, 34, 1, 522, 3, 15, 14, 1, 6, 2, 3, 1, 4, 5, 4, 10, 1}.

a(n) = 1 if and only if n is in A006254. (End)

From Eric Chen, Sep 16 2021: (Start)

Now a(303) is known to be 40174, also other terms > 10000: a(383) = 20956, a(515) = 58466, a(522) = 62288, a(578) = 129468, a(581) > 400000, a(590) = 15526, a(647) = 21576, a(662) = 16590, a(698) = 127558, a(704) = 62034, see the a-file and the references.

a(n) = 2 if and only if n is in A066049 but not in A006254.

a(n) = 3 if and only if n is in A214289 but not in A006254 or A066049. (End)

LINKS

Eric Chen, Table of n, a(n) for n = 2..580

Gary Barnes, Riesel conjectures and proofs

Eric Chen, Table of n, a(n) for n = 2..2050 status

Prime Wiki, Riesel prime small bases least n

FORMULA

From Eric Chen, Sep 16 2021: (Start)

a(6*n) = A098873(n).

a(2^n) = A279095(n).

a(A006254(n)) = 1.

a(A066049(n)) <= 2.

a(A214289(n)) <= 3. (End)

MATHEMATICA

f[n_] := Block[{k = 0}, While[ ! PrimeQ[2*n^k - 1], k++ ]; k ]; Table[f[n], {n, 2, 106}] (* Ray Chandler, Jun 08 2006 *)

PROG

(PARI) a(n) = for(k=1, 2^24, if(ispseudoprime(2*n^k-1), return(k))) \\ Eric Chen, Jun 01 2015

CROSSREFS

Cf. A119624, A253178.

Numbers r such that 2*k^r-1 is prime: A090748 (k=2), A003307 (k=3), A146768 (k=4), A120375 (k=5), A057472 (k=6), A002959 (k=7), ... (k=8), ... (k=9), A002957 (k=10), A120378 (k=11), ... (k=12), A174153 (k=13), A273517 (k=14), ... (k=15), ... (k=16), A193177 (k=17), A002958 (k=25).

Sequence in context: A363919 A368000 A335502 * A333782 A304876 A010125

Adjacent sequences: A119588 A119589 A119590 * A119592 A119593 A119594

KEYWORD

nonn,hard

AUTHOR

Pierre CAMI, Jun 01 2006

EXTENSIONS

Corrected and extended by Ray Chandler, Jun 08 2006

STATUS

approved