A228922 -id:A228922 - cp's OEIS frontend

A380253 Numbers k such that (25^k + 2^k)/27 is prime.

19, 109, 967, 2143, 11471, 11939

Offset: 1

Robert Price, Jan 17 2025

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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Select[Prime[Range[10000]], PrimeQ[(25^# + 2^#)/27] &]

A381092 Numbers k such that (43^k + 2^k)/45 is prime.

Original entry on oeis.org

31, 41, 61, 599, 1231, 1249, 35671

Offset: 1

Robert Price, Feb 13 2025

The definition implies that k must be a prime.

a(8) > 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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

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

A382866 Numbers k such that (49^k + 2^k)/51 is prime.

Original entry on oeis.org

13, 307, 1187, 9241, 94321

Offset: 1

Robert Price, Jun 11 2025

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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Select[Prime[Range[10000]], PrimeQ[(49^# + 2^#)/51] &]

A385244 Numbers k such that (33^k + 2^k)/35 is prime.

Original entry on oeis.org

47, 269, 2287, 5059

Offset: 1

Robert Price, Jul 28 2025

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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

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

A386383 Numbers k such that (22^k + 3^k)/25 is prime.

Original entry on oeis.org

2617, 3739, 14207, 43789

Offset: 1

Robert Price, Aug 17 2025

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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Select[Prime[Range[10000]], PrimeQ[(22^# + 3^#)/25] &]

A387390 Numbers k such that (28^k + 3^k)/31 is prime.

Original entry on oeis.org

3, 17, 443, 3907, 18911, 50929

Offset: 1

Robert Price, Aug 28 2025

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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Select[Prime[Range[10000]], PrimeQ[(28^# + 3^#)/31] &]

A387392 Numbers k such that (29^k + 3^k)/32 is prime.

Original entry on oeis.org

11, 181, 229, 311, 701, 4493, 5233, 13879

Offset: 1

Robert Price, Aug 28 2025

The definition implies that k must be a prime.

a(9) > 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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Select[Prime[Range[10000]], PrimeQ[(29^# + 3^#)/32] &]

A387473 Numbers k such that (31^k + 3^k)/34 is prime.

Original entry on oeis.org

3, 5, 313, 677

Offset: 1

Robert Price, Aug 30 2025

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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Select[Prime[Range[10000]], PrimeQ[(31^# + 3^#)/34] &]

A387474 Numbers k such that (32^k + 3^k)/35 is prime.

Original entry on oeis.org

3, 47, 107, 157, 4799, 21841

Offset: 1

Robert Price, Aug 30 2025

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.
OEIS Wiki, Primes of the form (a^n+b^n)/(a+b) and (a^n-b^n)/(a-b)

Cf. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Select[Prime[Range[10000]], PrimeQ[(32^# + 3^#)/35] &]

cp's OEIS Frontend

A380253 Numbers k such that (25^k + 2^k)/27 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A381092 Numbers k such that (43^k + 2^k)/45 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A382866 Numbers k such that (49^k + 2^k)/51 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A385244 Numbers k such that (33^k + 2^k)/35 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A386383 Numbers k such that (22^k + 3^k)/25 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A387390 Numbers k such that (28^k + 3^k)/31 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A387392 Numbers k such that (29^k + 3^k)/32 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A387473 Numbers k such that (31^k + 3^k)/34 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A387474 Numbers k such that (32^k + 3^k)/35 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs