A194606 - OEIS

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

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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 *)