A086661 -id:A086661 - 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", ")))

A230769 Numbers k such that (k+1)*2^k - 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 9, 14, 15, 16, 27, 45, 122, 125, 213, 242, 256, 263, 290, 855, 1059, 2273, 3945, 3999, 9512, 14127, 16486, 20056, 28834, 41493, 159147, 227139, 587823

Offset: 1

Zak Seidov, Feb 23 2014

1, 2 and 5 are the only terms of this sequence which are also in A029544. - Gerasimov Sergey, Feb 23 2014
The next term with this property is > 10000. - Michael B. Porter, Feb 23 2014
The probability of a given number N being a twin prime grows like 1/(log(N))^2, so for a given n, the probability that it has this property is 1/n^2, and the sum converges.  Are there any n for which n*2^n-1 and n*2^n+1 are both prime? - Michael B. Porter, Feb 25 2014
We can write (k+1)*2^k - 1 = {(k+1)/2}*4^{(k+1)/2} - 1, and when k is odd, this takes the form of a generalized Woodall prime (base 4). These are listed in A086661. In other words, {2*A086661 - 1} gives all the odd terms of this sequence. - Jeppe Stig Nielsen, Oct 16 2019
The largest odd term currently known is 3986381 = 2*A086661(21) - 1. - Jeppe Stig Nielsen, Oct 16 2019

Steven Harvey, NearCullen and NearWoodall Primes
Prime-Wiki, Near Generalized Woodall primes of the form (n+1)*2^n - 1

Cf. A029544, A086661, A196273, A236752.

is_A230769(n) = ispseudoprime((n+1)*2^n-1) \\ M. F. Hasler, Mar 01 2014

Edited and extended to values > 2273 by M. F. Hasler, Mar 01 2014

More terms from Jeppe Stig Nielsen, Oct 16 2019

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

A242335 Numbers k such that k*4^k-1 is semiprime.

Original entry on oeis.org

10, 12, 18, 24, 27, 44, 47, 65, 71, 82, 84, 131, 134, 138, 143, 155, 164, 168, 197, 212, 227, 243, 248, 293, 302, 384, 401

Offset: 1

Vincenzo Librandi, May 12 2014

nonn

The semiprimes of this form are: 10485759, 201326591, 1236950581247, 6755399441055743, 486388759756013567, 13617340432139183023890366463, ...

Cf. similar sequences listed in A242273.

Cf. A060416, A086661.

IsSemiprime:=func; [n: n in [2..100] | IsSemiprime(s) where s is n*4^n-1];

Mathematica

Select[Range[100], PrimeOmega[# 4^# - 1]==2&]

PARI

isok(n)=bigomega(n*4^n-1)==2 \\ Anders Hellström, Aug 18 2015

Extensions

a(12)-a(16) from Carl Schildkraut, Aug 18 2015

a(17)-a(27) from Charles R Greathouse IV, Aug 18 2015

cp's OEIS Frontend

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

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Magma

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A230769 Numbers k such that (k+1)*2^k - 1 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Extensions

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

Examples

Links

Crossrefs

Programs

Mathematica

A242335 Numbers k such that k*4^k-1 is semiprime.

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Author

Keywords

Comments

Crossrefs

Programs

Magma

Mathematica

PARI

Extensions