A194606 Least k >= 0 such that prime(n)*2^k - 1 or prime(n)*2^k + 1 is prime, or -1 if no such value exists, where prime(n) denotes the n-th prime number.

0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 4, 1, 5, 3, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 6, 1, 2, 1, 2, 1, 3, 4, 1, 2, 4, 1, 1, 3, 1, 2, 2, 1, 1, 3, 2, 1, 1, 1, 11, 1, 4, 2, 3, 1, 2, 1, 11, 1, 1, 9, 3, 6, 1, 1, 3, 3, 4, 1, 1, 2, 1, 2, 11, 4, 3, 2, 1, 4, 1, 2, 1, 1

Offset

1,6

Comments

A194607 gives the record values.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Brier Number

Example

For n=4, 7*2^0-1 and 7*2^0+1 are composite, but 7*2^1-1=13 is prime, so a(4)=1.

Mathematica

Table[p = Prime[n]; k = 0; While[! PrimeQ[p*2^k - 1] && ! PrimeQ[p*2^k + 1], k++]; k, {n, 100}] (* Arkadiusz Wesolowski, Sep 04 2011 *)

Crossrefs

Cf. A194591, A194600, A194603, A194607, A194608, A194635, A194636, A194637, A194638, A194639.

Cf. A040081, A040076, A076335, A180247.

Sequence in context: A341356 A276153 A341348 * A331180 A126389 A278112

Adjacent sequences: A194603 A194604 A194605 * A194607 A194608 A194609

Keyword

sign

Author

Arkadiusz Wesolowski, Aug 30 2011

Status

approved