A217320 -id:A217320 - cp's OEIS frontend

A375161 Numbers k such that (23^k - 2^k)/21 is prime.

Original entry on oeis.org

5, 11, 197, 4159

Offset: 1

Robert Price, Aug 04 2024

The definition implies that k must be a prime.

a(5) > 10^5.

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
P. Bourdelais, A Generalized Repunit Conjecture
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542.

Select[Prime[Range[100]], PrimeQ[(23^# - 2^#)/21] &]

A225807 Numbers n such that (17^n - 2^n)/15 is prime.

Original entry on oeis.org

2, 83, 1907, 2591, 16223, 17183

Offset: 1

Robert Price, Jul 29 2013

All terms are primes.

a(7) > 10^5.

Cf. A128031, A225955, A217320, A006034.

Select[ Prime[ Range[1, 100000] ], PrimeQ[ (17^# - 2^#)/15 ]& ]

is(n)=ispseudoprime((17^n-2^n)/15) \\ Charles R Greathouse IV, Jun 06 2017

A375236 Numbers k such that (21^k - 2^k)/19 is prime.

Original entry on oeis.org

2, 3, 353, 751, 9587

Offset: 1

Robert Price, Aug 06 2024

The definition implies that k must be a prime.

a(6) > 10^5.

P. Bourdelais, A Generalized Repunit Conjecture.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161.

Select[Prime[Range[100]], PrimeQ[(21^# - 2^#)/19] &]

A377031 Numbers k such that (27^k - 2^k)/25 is prime.

Original entry on oeis.org

2, 3, 269, 401, 631, 701, 1321, 2707, 5471, 6581

Offset: 1

Robert Price, Oct 13 2024

The definition implies that k must be a prime.

a(11) > 10^5.

P. Bourdelais, A Generalized Repunit Conjecture.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236.

Select[Prime[Range[1000]], PrimeQ[(27^# - 2^#)/25] &]

A377856 Numbers k such that (21^k + 2^k)/23 is prime.

Original entry on oeis.org

11, 17, 47, 2663

Offset: 1

Robert Price, Nov 09 2024

The definition implies that k must be a prime.

a(5) > 10^5.

P. Bourdelais, A Generalized Repunit Conjecture.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(21^# + 2^#)/23] &]

A225955 Numbers n such that (15^n - 2^n)/13 is prime.

Original entry on oeis.org

2, 5, 11, 167, 317, 337, 349, 3449, 7517, 23003

Offset: 1

Robert Price, May 21 2013

All terms are primes.

a(11) > 2*10^5.

Cf. A128028, A016054, A217320, A006033.

Select[ Prime[ Range[1, 100000] ], PrimeQ[ (15^# - 2^#)/13 ]& ]

is(n)=ispseudoprime((15^n-2^n)/13) \\ Charles R Greathouse IV, May 22 2017

A376329 Numbers k such that (45^k - 2^k)/43 is prime.

Original entry on oeis.org

2, 7, 89, 167, 8101, 96517

Offset: 1

Robert Price, Nov 19 2024

The definition implies that k must be a prime.

a(7) > 10^5.

P. Bourdelais, A Generalized Repunit Conjecture.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(45^# - 2^#)/43] &]

A376470 Numbers k such that (29^k - 2^k)/27 is prime.

Original entry on oeis.org

2, 7, 139, 983, 3257, 10181, 26387, 36187, 42557

Offset: 1

Robert Price, Sep 24 2024

The definition implies that k must be a prime.

a(10) > 10^5.

P. Bourdelais, A Generalized Repunit Conjecture.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236.

Select[Prime[Range[1000]], PrimeQ[(29^# - 2^#)/27] &]

A377180 Numbers k such that (43^k - 2^k)/41 is prime.

Original entry on oeis.org

167, 797, 1009, 54941

Offset: 1

Robert Price, Oct 18 2024

The definition implies that k must be a prime.

a(5) > 10^5.

P. Bourdelais, A Generalized Repunit Conjecture.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(43^# - 2^#)/41] &]

A377699 Numbers k such that (35^k - 2^k)/33 is prime.

Original entry on oeis.org

2, 17, 53, 211, 4013, 55207

Offset: 1

Robert Price, Nov 05 2024

The definition implies that k must be a prime.

a(7) > 10^5.

P. Bourdelais, A Generalized Repunit Conjecture.
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit.

Cf. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(35^# - 2^#)/33] &]

cp's OEIS Frontend

A375161 Numbers k such that (23^k - 2^k)/21 is prime.

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A225807 Numbers n such that (17^n - 2^n)/15 is prime.

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A375236 Numbers k such that (21^k - 2^k)/19 is prime.

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A377031 Numbers k such that (27^k - 2^k)/25 is prime.

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A377856 Numbers k such that (21^k + 2^k)/23 is prime.

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A225955 Numbers n such that (15^n - 2^n)/13 is prime.

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PARI

A376329 Numbers k such that (45^k - 2^k)/43 is prime.

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Mathematica

A376470 Numbers k such that (29^k - 2^k)/27 is prime.

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Mathematica

A377180 Numbers k such that (43^k - 2^k)/41 is prime.

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