A377031 -id:A377031 - cp's OEIS frontend

A378953 Numbers k such that (29^k + 2^k)/31 is prime.

3, 7, 11, 157, 1429, 2579, 11909

Offset: 1

Robert Price, Dec 11 2024

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.

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

Select[Prime[Range[10000]], PrimeQ[(29^# + 2^#)/31] &]

A379428 Numbers k such that (39^k + 2^k)/41 is prime.

Original entry on oeis.org

3, 5, 19, 2543, 4691, 14669, 19819, 53891, 83137

Offset: 1

Robert Price, Dec 22 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. A057187, A057188, A062587, A062589, A127996, A127997, A128344, A204940, A217320, A225807, A228922, A229542, A375161, A375236, A377031, A377856.

Select[Prime[Range[10000]], PrimeQ[(39^# + 2^#)/41] &]

A379429 Numbers k such that (31^k + 2^k)/33 is prime.

Original entry on oeis.org

229, 1429, 36083, 44089

Offset: 1

Robert Price, Dec 22 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, A377856.

Select[Prime[Range[10000]], PrimeQ[(31^# + 2^#)/33] &]

A379986 Numbers k such that (20^k + 3^k)/23 is prime.

Original entry on oeis.org

3, 19, 271, 577, 977, 1871, 8647, 9479, 34759, 44959, 63149

Offset: 1

Robert Price, Jan 07 2025

The definition implies that k must be a prime.

a(12) > 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[(20^# + 3^#)/23] &]

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

Original entry on oeis.org

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] &]

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] &]

cp's OEIS Frontend

A378953 Numbers k such that (29^k + 2^k)/31 is prime.

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A379428 Numbers k such that (39^k + 2^k)/41 is prime.

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A379429 Numbers k such that (31^k + 2^k)/33 is prime.

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A379986 Numbers k such that (20^k + 3^k)/23 is prime.

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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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Mathematica

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

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Mathematica

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

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