A062647 Numbers k such that 81^k - 80^k is prime.

3, 43, 113, 157, 269, 709, 1109, 2027, 8297, 86837, 310721

Offset

1,1

Comments

Terms greater than 1000 are often only strong pseudoprimes.

a(11) > 10^5. - Robert Price, Jan 13 2015

Factors of these numbers are of the form p = 2*n*k + 1, just like the repunit numbers, but the PRP tests are significantly slower since there is not a fast mod() property like the repunits, where (number mod Rn) can be calculated with a folding of the digits at length n in base b. However, numbers of this form b^p - (b-1)^p seem to be prime with greater relative frequency than the repunits. While the repunits have a linear fit coefficient that approaches 0.56145948 (see link below for a Generalized Repunit Conjecture), this sequence currently has a linear fit coefficient of 0.22559. - Paul Bourdelais, Jul 06 2023

Links

Table of n, a(n) for n=1..11.

Paul Bourdelais, A Generalized Repunit Conjecture

Prog

(PARI) is(n)=ispseudoprime(81^n-80^n) \\ Charles R Greathouse IV, Jun 12 2017

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062666.

Sequence in context: A199348 A002551 A127930 * A003525 A042661 A281503

Adjacent sequences: A062644 A062645 A062646 * A062648 A062649 A062650

Keyword

nonn,hard,more

Author

Mike Oakes, May 18 2001, May 19 2001

Extensions

a(10) from Robert Price, Jan 13 2015 (Computer run by Adam Marciniec)

a(11) from Paul Bourdelais, Jul 06 2023

Status

approved