A006553 -id:A006553 - 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

A242274 Numbers k such that k*3^k - 1 is semiprime.

Original entry on oeis.org

4, 5, 8, 12, 20, 24, 25, 28, 32, 38, 42, 44, 60, 62, 66, 70, 72, 80, 122, 125, 148, 228, 244, 270, 389, 390, 432, 464, 470, 488, 549, 560, 804, 862

Offset: 1

Vincenzo Librandi, May 12 2014

The semiprimes of this form are 323, 1214, 52487, 6377291, 69735688019, 6778308875543, 21182215236074, 640550188738907, 59296646043258911, ...
804 is a term of this sequence. - Luke March, Aug 22 2015
The smallest unresolved value of k is now 862. - Sean A. Irvine, Jun 20 2022
The smallest unresolved value of k is now 866. - Tyler Busby, Oct 06 2023
From Jon E. Schoenfield, Oct 06 2023: (Start)
After the possible term 866, the only remaining 3-digit terms are 912 and 984, unless 920 is a term.
If k is an odd term, then k*3^k - 1 is even, so (k*3^k - 1)/2 is a prime. The next odd terms after 549 are 1125 and 12889. Odd terms are in A366323. (End)
26925 is a term. - Michael S. Branicky, Oct 08 2024

Cf. similar sequence listed in A242273.

Cf. A006553, A060352, A366323.

IsSemiprime:=func; [n: n in [2..241] | IsSemiprime(s) where s is n*3^n-1];

Mathematica

Select[Range[241], PrimeOmega[# 3^# - 1]==2&]

PARI

isok(n)=bigomega(n*3^n-1)==2 /* Anders Hellström, Aug 18 2015 */

Extensions

a(21)-a(23) from Carl Schildkraut, Aug 18 2015

a(24)-a(32) from Luke March, Aug 22 2015

a(32) = 804 removed by Sean A. Irvine, Apr 25 2022

a(32)-a(33) from Sean A. Irvine, Jun 20 2022

a(34) from Tyler Busby, Oct 06 2023

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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A242274 Numbers k such that k*3^k - 1 is semiprime.

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Magma

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A271956 Numbers n such that 2*n*3^n - 1 is prime.

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Maple

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A271956 Numbers n such that 2n3^n - 1 is prime.