A204940 -id:A204940 - cp's OEIS frontend

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

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] &]

A384736 Numbers k such that (28^k - 3^k)/25 is prime.

Original entry on oeis.org

2, 3, 7, 43, 197, 13397, 28837, 29153

Offset: 1

Robert Price, Jun 08 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. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(28^# - 3^#)/25] &]

A384767 Numbers k such that (29^k - 3^k)/26 is prime.

Original entry on oeis.org

3, 7, 17, 1069, 28081, 66509, 91493

Offset: 1

Robert Price, Jun 09 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. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(29^# - 3^#)/26] &]

A384925 Numbers k such that (32^k - 3^k)/29 is prime.

Original entry on oeis.org

3, 19, 37, 233, 283, 311, 1307, 1913

Offset: 1

Robert Price, Jun 12 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. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

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

A384972 Numbers k such that (25^k - 3^k)/22 is prime.

Original entry on oeis.org

3, 5, 43, 709, 1151, 3323, 3643, 4637, 21661

Offset: 1

Robert Price, Jun 13 2025

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

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

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

A385064 Numbers k such that (31^k - 3^k)/28 is prime.

Original entry on oeis.org

3, 23, 53, 661, 8923, 9721, 13807

Offset: 1

Robert Price, Jun 16 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. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

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

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] &]

A385518 Numbers k such that (37^k - 3^k)/34 is prime.

Original entry on oeis.org

3, 137, 197, 2113, 4729, 11497

Offset: 1

Robert Price, Jul 01 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. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(37^# - 3^#)/34] &]

A385680 Numbers k such that (40^k - 3^k)/37 is prime.

Original entry on oeis.org

2, 5, 1549, 4391

Offset: 1

Robert Price, Aug 04 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. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(40^# - 3^#)/37] &]

A385684 Numbers k such that (38^k - 3^k)/35 is prime.

Original entry on oeis.org

2, 3, 19, 101, 229, 1031, 2393, 3121, 4021

Offset: 1

Robert Price, Jul 06 2025

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

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

Select[Prime[Range[10000]], PrimeQ[(38^# - 3^#)/35] &]

cp's OEIS Frontend

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

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A384736 Numbers k such that (28^k - 3^k)/25 is prime.

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A384767 Numbers k such that (29^k - 3^k)/26 is prime.

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A384925 Numbers k such that (32^k - 3^k)/29 is prime.

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A384972 Numbers k such that (25^k - 3^k)/22 is prime.

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A385064 Numbers k such that (31^k - 3^k)/28 is prime.

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

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A385518 Numbers k such that (37^k - 3^k)/34 is prime.

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A385680 Numbers k such that (40^k - 3^k)/37 is prime.

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