A204940 -id:A204940 - cp's OEIS frontend

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

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] &]

A380355 Numbers k such that (47^k - 2^k)/45 is prime.

Original entry on oeis.org

17, 103, 773, 2467, 41969

Offset: 1

Robert Price, Jan 22 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. A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A229542, A375161, A375236, A377031.

Select[Prime[Range[10000]], PrimeQ[(47^# - 2^#)/45] &]

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] &]

A381093 Numbers k such that (26^k - 3^k)/23 is prime.

Original entry on oeis.org

2, 31, 263, 743, 1439, 6661, 78593

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

Select[Prime[Range[10000]], PrimeQ[(26^# - 3^#)/23] &]

A381200 Numbers k such that (49^k - 2^k)/47 is prime.

Original entry on oeis.org

3, 5, 29, 89, 35279

Offset: 1

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

Select[Prime[Range[10000]], PrimeQ[(49^# - 2^#)/47] &]

A381338 Numbers k such that (22^k - 3^k)/19 is prime.

Original entry on oeis.org

5, 31, 823, 15287, 26293, 32083, 51263, 92791

Offset: 1

Robert Price, Feb 20 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[(22^# - 3^#)/19] &]

A382391 Numbers k such that (23^k - 3^k)/20 is prime.

Original entry on oeis.org

3, 7, 31, 47, 109, 151, 223, 463, 739, 6427, 17581, 30517

Offset: 1

Robert Price, Mar 23 2025

The definition implies that k must be a prime.

a(13) > 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[(23^# - 3^#)/20] &]

cp's OEIS Frontend

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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A380355 Numbers k such that (47^k - 2^k)/45 is prime.

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

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A381093 Numbers k such that (26^k - 3^k)/23 is prime.

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A381200 Numbers k such that (49^k - 2^k)/47 is prime.

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Mathematica

A381338 Numbers k such that (22^k - 3^k)/19 is prime.

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