A057188 -id:A057188 - cp's OEIS frontend

A379987 Numbers k such that (35^k + 2^k)/37 is prime.

5, 1217, 2029, 5171, 5651, 23633, 41179, 71069

Offset: 1

Robert Price, Jan 07 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.

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

Select[Prime[Range[10000]], PrimeQ[(35^# + 2^#)/37] &]

A379988 Numbers k such that (27^k + 2^k)/29 is prime.

Original entry on oeis.org

11, 2297, 2707, 3187

Offset: 1

Robert Price, Jan 07 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.

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

Select[Prime[Range[10000]], PrimeQ[(27^# + 2^#)/29] &]

A380131 Numbers k such that (45^k + 2^k)/47 is prime.

Original entry on oeis.org

17, 281, 463, 5393, 12809, 19031, 53173

Offset: 1

Robert Price, Jan 12 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[(45^# + 2^#)/47] &]

A380132 Numbers k such that (47^k + 2^k)/49 is prime.

Original entry on oeis.org

11, 13, 103, 15383

Offset: 1

Robert Price, Jan 12 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[(47^# + 2^#)/49] &]

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

Original entry on oeis.org

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] &]

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A379987 Numbers k such that (35^k + 2^k)/37 is prime.

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A379988 Numbers k such that (27^k + 2^k)/29 is prime.

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A380131 Numbers k such that (45^k + 2^k)/47 is prime.

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A380132 Numbers k such that (47^k + 2^k)/49 is prime.

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

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

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

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Mathematica

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

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

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