A062583 -id:A062583

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A062585

Numbers k such that 19^k - 18^k is prime.

+10
4

2, 1607, 1873, 10957

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

PrimePi[ a(n) ] = {2, 253, 287, 1331, ...}. - Alexander Adamchuk, Feb 16 2007

a(5) > 10^5. - Robert Price, Jun 05 2012

Terms greater than 1000 may correspond to (unproven) strong pseudoprimes. - M. F. Hasler, Sep 16 2013

LINKS

Table of n, a(n) for n=1..4.

PROG

(PARI) is(n)=ispseudoprime(19^n-18^n) \\ Charles R Greathouse IV, Feb 20 2017

CROSSREFS

Cf. A000043, A057468, A059801, A059802, A062572-A062583, A188051, A062586-A062666.

KEYWORD

nonn,hard

AUTHOR

Mike Oakes, May 18 2001, May 19 2001

EXTENSIONS

10957 (found by Mike Oakes in 2003) from Alexander Adamchuk, Feb 16 2007

STATUS

approved

A188051

Numbers k such that 18^k - 17^k is prime, or a strong pseudoprime.

+10
2

3, 13, 71, 14533, 26641, 48179

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Terms < 10000 found by Mike Oakes.

Term 14533 found by Lelio R Paula in June 2008 corresponding to a probable prime with 18243 digits.

Terms 26641 and 48179 found by Jean-Louis Charton in December 2010 corresponding to probable primes with 33442 and 60478 digits.

a(7) > 10^5. - Robert Price, Nov 30 2012

LINKS

Table of n, a(n) for n=1..6.

Top probable primes of the form 18^p-17^p

PROG

(PARI) is(n)=ispseudoprime(18^n-17^n) \\ Charles R Greathouse IV, Jun 06 2017

CROSSREFS

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062583, A062585-A062666.

KEYWORD

nonn,hard

AUTHOR

Jean-Louis Charton, Mar 19 2011

EXTENSIONS

Edited by M. F. Hasler, Sep 21 2013

STATUS

approved

A219284

Primes of the form 17^n - 16^n.

+10
1

371281, 141903217

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

a(3) has 98 digits and a(6) has 3491 digits.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5

MATHEMATICA

Select[Table[17^n - 16^n, {n, 0, 300}], PrimeQ]

PROG

(Magma) [a: n in [0..30] | IsPrime(a) where a is 17^n - 16^n];

CROSSREFS

Cf. A062583.

KEYWORD

nonn,bref

AUTHOR

Vincenzo Librandi, Nov 24 2012

STATUS

approved

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