A062589 -id:A062589 - 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] &]

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] &]

A062592 Numbers k such that 26^k - 25^k is prime or a strong pseudoprime.

Original entry on oeis.org

3, 7, 97, 109, 401, 431

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

a(7) > 10^5. - Robert Price, Nov 10 2012

Cf. A000043, A057468, A059801, A059802, A062572-A062589, A214658, A214655, A062593-A062666.

Edited by M. F. Hasler, Sep 21 2013

A214655 Numbers n such that 25^n - 24^n is prime or a strong pseudoprime.

Original entry on oeis.org

3, 5, 29, 54799

Offset: 1

Robert Price, Jul 24 2012

All terms are prime.

No other terms less than 10^5. - Robert Price, Jul 24 2012

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062589, A214658, A062592-A062666.

Select[Range[10^5], PrimeQ[25^#-24^# ]&]

Edited by M. F. Hasler, Sep 21 2013

A214658 Numbers n such that 24^n - 23^n is prime or a strong pseudoprime.

Original entry on oeis.org

2, 3, 31, 40519, 51061

Offset: 1

Robert Price, Jul 24 2012

All terms are prime.

No other terms less than 10^5. - Robert Price, Jul 24 2012

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062589, A214655, A062592-A062666.

Select[Range[10^5], PrimeQ[24^#-23^# ]&]

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] &]

cp's OEIS Frontend

A375161 Numbers k such that (23^k - 2^k)/21 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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A062592 Numbers k such that 26^k - 25^k is prime or a strong pseudoprime.

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A214655 Numbers n such that 25^n - 24^n is prime or a strong pseudoprime.

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A214658 Numbers n such that 24^n - 23^n is prime or a strong pseudoprime.

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

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

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