A002234 -id:A002234 - cp's OEIS frontend

A299377 Numbers k such that k * 14^k - 1 is prime.

1, 3, 7, 98, 104, 128, 180, 834, 1633, 8000, 28538, 46605, 131941, 147684, 433734

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(16) > 500000.

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), this sequence (b=14), A299378 (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*14^n-1)];

Select[Range[1, 10000], PrimeQ[n*14^n-1] &]

for(n=1, 10000, if(isprime(n*14^n-1), print1(n", ")))

A299378 Numbers k such that k * 15^k - 1 is prime.

Original entry on oeis.org

2, 10, 14, 2312, 16718, 26906, 27512, 41260, 45432, 162454, 217606

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(12) > 500000.

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), this sequence (b=15), A299379 (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*15^n-1)];

Select[Range[1, 10000], PrimeQ[n*15^n-1] &]

for(n=1, 10000, if(isprime(n*15^n-1), print1(n", ")))

A299379 Numbers k such that k * 16^k - 1 is prime.

Original entry on oeis.org

167, 189, 639

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(4) > 500000.

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), this sequence (b=16), A299380 (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*16^n-1)];

Select[Range[1, 10000], PrimeQ[n*16^n-1] &]

for(n=1, 10000, if(isprime(n*16^n-1), print1(n", ")))

A299380 Numbers k such that k * 17^k - 1 is prime.

Original entry on oeis.org

2, 18, 20, 38, 68, 3122, 3488, 39500

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(9) > 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), this sequence (b=17), A299381 (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*17^n-1)];

Select[Range[1, 10000], PrimeQ[n*17^n-1] &]

for(n=1, 10000, if(isprime(n*17^n-1), print1(n", ")))

A299381 Numbers k such that k * 18^k - 1 is prime.

Original entry on oeis.org

1, 2, 6, 8, 10, 28, 30, 39, 45, 112, 348, 380, 458, 585, 17559, 38751, 43346, 46984, 92711

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(20) > 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), this sequence (b=18), A299382 (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*18^n-1)];

Select[Range[1, 10000], PrimeQ[n*18^n-1] &]

for(n=1, 10000, if(isprime(n*18^n-1), print1(n", ")))

A299382 Numbers k such that k * 19^k - 1 is prime.

Original entry on oeis.org

12, 410, 33890, 91850, 146478, 189620, 280524

Offset: 1

Tim Johannes Ohrtmann, Feb 08 2018

a(8) > 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), this sequence (b=19), A299383 (b=20).

[n: n in [1..10000] |IsPrime(n*19^n-1)];

Select[Range[1, 10000], PrimeQ[n*19^n-1] &]

for(n=1, 10000, if(isprime(n*19^n-1), print1(n", ")))

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

Original entry on oeis.org

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", ")))

A367037 Numbers k such that k^3*2^k - 1 is a prime.

Original entry on oeis.org

2, 8, 31, 79, 661, 769, 1904, 2527, 9032, 15895, 19171

Offset: 1

Juri-Stepan Gerasimov, Nov 02 2023

If it exists, a(12) > 100000. - Hugo Pfoertner, Nov 03 2023

Numbers k such that k^m*2^k - 1 is prime: A000043 (m = 0), A002234 (m = 1), A058781 (m = 2), this sequence (m = 3).

[k: k in [1..700] | IsPrime(k^3*2^k-1)];

Select[Range[3000], PrimeQ[#^3*2^# - 1] &] (* Amiram Eldar, Nov 04 2023 *)

a(11) from Hugo Pfoertner, Nov 02 2023

A367102 Numbers k such that k^4*2^k - 1 is a prime.

Original entry on oeis.org

3, 29, 43, 83, 133, 209, 271, 329, 415, 727, 2437, 5673, 6879, 7813, 8125, 11931, 29433, 29491, 38397, 91141, 99459, 110935, 127247

Offset: 1

Juri-Stepan Gerasimov, Nov 04 2023

Numbers k such that k^m*2^k - 1 is prime: A000043 (m = 0), A002234 (m = 1), A058781 (m = 2), A367037 (m = 3), this sequence (m = 4).

[k: k in [1..500] | IsPrime(k^4*2^k-1)];

Select[Range[6000], PrimeQ[#^4*2^# - 1] &] (* Amiram Eldar, Nov 05 2023 *)

a(17)-a(18) from Amiram Eldar, Nov 05 2023
a(19) from Michael S. Branicky, Nov 05 2023
a(20)-a(23) from Hugo Pfoertner, Nov 08 2023, Nov 10 2023

A257379 Smallest odd number k such that kn2^n - 1 is a prime number.

Original entry on oeis.org

3, 1, 1, 3, 3, 1, 3, 3, 5, 5, 9, 5, 7, 7, 3, 17, 11, 11, 7, 9, 11, 15, 3, 7, 9, 67, 3, 45, 3, 1, 33, 21, 15, 23, 17, 3, 7, 9, 19, 15, 17, 63, 51, 3, 9, 33, 53, 61, 13, 45, 75, 39, 83, 43, 7, 19, 13, 41, 5, 19, 31, 165, 13, 27, 3, 13, 135, 33, 31, 15, 33, 87

Offset: 1

Pierre CAMI, Apr 21 2015

nonn

Conjecture: a(n) exists for every n.
The conjecture follows from Dirichlet's theorem on primes in arithmetic progressions. - Robert Israel, Jan 05 2016
As N increases, (Sum_{n=1..N} k) / (Sum_{n=1..N} n) approaches 0.833.
If k=1 then n*2^n-1 is a Woodall prime (see A002234).
Generalized Woodall primes have the form n*b^n-1, I propose to name the primes k*n*2^n-1 generalized Woodall primes of the second type.

			1*1*2^1 - 1 = unity, 3*1*2^1 - 1 = 5, which is prime, so a(1) = 3.
1*2*2^2 - 1 = 7, which is prime, so a(2) = 1.
1*3*2^3 - 1 = 23, which is prime, so a(3) = 1.

Pierre CAMI, Table of n, a(n) for n = 1..10000

Cf. A002234, A256787, A257378, A266909.

Q:= proc(m) local k;
  for k from 1 by 2 do if isprime(k*m-1) then return k fi od
end proc:
seq(Q(n*2^n),n=1..100); # Robert Israel, Jan 05 2016

Table[k = 1; While[!PrimeQ[k*n*2^n - 1], k += 2]; k, {n, 72}] (* Michael De Vlieger, Apr 21 2015 *)

a(n) = k=1; while(!isprime(k*n*2^n-1), k+=2); k \\ Colin Barker, Apr 21 2015

cp's OEIS Frontend

A299377 Numbers k such that k * 14^k - 1 is prime.

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A299378 Numbers k such that k * 15^k - 1 is prime.

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Magma

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A299379 Numbers k such that k * 16^k - 1 is prime.

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Magma

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A299380 Numbers k such that k * 17^k - 1 is prime.

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Magma

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A299381 Numbers k such that k * 18^k - 1 is prime.

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Magma

Mathematica

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A299382 Numbers k such that k * 19^k - 1 is prime.

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Magma

Mathematica

PARI

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

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Programs

Magma

Mathematica

PARI

A367037 Numbers k such that k^3*2^k - 1 is a prime.

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A257379 Smallest odd number k such that kn2^n - 1 is a prime number.