A059675 -id:A059675 - cp's OEIS frontend

A299383 Numbers k such that k * 20^k - 1 is prime.

1, 18, 44, 60, 80, 123, 429, 1166, 2065, 8774, 35340, 42968, 50312, 210129

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(15) > 400000.

Steven Harvey, Generalized Woodall Search
Wikipedia, Woodall number

Numbers n such that n * b^n - 1 is prime: A008864 (b=1), A002234 (b=2), A006553 (b=3), A086661 (b=4), A059676 (b=5), A059675 (b=6), A242200 (b=7), A242201 (b=8), A242202 (b=9), A059671 (b=10), A299374 (b=11), A299375 (b=12), A299376 (b=13), A299377 (b=14), A299378 (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), this sequence (b=20).

[n: n in [1..10000] |IsPrime(n*20^n-1)];

Select[Range[1, 10000], PrimeQ[n*20^n-1] &]

for(n=1, 10000, if(isprime(n*20^n-1), print1(n", ")))

A210340 Generalized Woodall primes: any primes that can be written in the form n*b^n - 1 with n+2 > b > 2.

Original entry on oeis.org

17, 191, 4373, 5119, 524287, 590489, 3124999, 14680063, 3758096383, 6973568801, 34867844009, 85449218749, 824633720831, 1099999999999, 1618481116086271, 11577835060199423, 14999999999999999, 29311444762388081, 73123168801259519

Offset: 1

Arkadiusz Wesolowski, Mar 20 2012

nonn

			167*2^668 - 1 is a prime number and 167*2^668 - 1 = 167*16^167 - 1, so this number is in the sequence.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..170
Chris Caldwell, The Top 20 Generalized Woodall Primes
Chris Caldwell, The Prime Glossary, Woodall prime
G. L. Honaker, Jr. and Chris Caldwell, 17962...40287 (1006-digits)
G. L. Honaker, Jr. and Chris Caldwell, 19981...99999 (10028-digits)
PrimeGrid, Home Page
Wikipedia, Woodall number

Cf. A050918, A002234, A006553, A086661, A059676, A059675.

lst = {}; Do[p = n*b^n - 1; If[p < 10^200 && PrimeQ[p], AppendTo[lst, p]], {b, 3, 100}, {n, b - 1, 413}]; Sort@lst

A242337 Numbers k such that k*6^k - 1 is semiprime.

Original entry on oeis.org

4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 18, 22, 23, 25, 32, 35, 38, 45, 51, 54, 57, 68, 72, 82, 97, 110, 138, 155, 234, 254

Offset: 1

Vincenzo Librandi, May 12 2014

The semiprimes of this form are 5183, 38879, 279935, 1959551, 90699263, 604661759, 3990767615, 26121388031, 169789022207, 1097098297343, ...

a(32) >= 423. - Tyler Busby, Mar 19 2023

factordb.com, Status of 423*6^423-1.

Cf. similar sequences listed in A242273.

Cf. A059675, A064752.

IsSemiprime:=func; [n: n in [2..352] | IsSemiprime(s) where s is n*6^n-1];

Mathematica

Select[Range[352], PrimeOmega[# 6^# - 1]==2&]

Extensions

a(26)-a(31) from Carl Schildkraut, Aug 17 2015

cp's OEIS Frontend

A299383 Numbers k such that k * 20^k - 1 is prime.

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A210340 Generalized Woodall primes: any primes that can be written in the form n*b^n - 1 with n+2 > b > 2.

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Author

Keywords

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Links

Crossrefs

Programs

Mathematica

A242337 Numbers k such that k*6^k - 1 is semiprime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Extensions