A229524 -id:A229524 - cp's OEIS frontend

A229663 Numbers n such that (40^n + 1)/41 is prime.

53, 67, 1217, 5867, 6143, 11681, 29959

Offset: 1

Robert Price, Sep 27 2013

All terms are primes.

a(8) > 10^5.

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. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524.

Do[ p=Prime[n]; If[ PrimeQ[ (40^p + 1)/41 ], Print[p] ], {n, 1, 9592} ]

is(n)=ispseudoprime((40^n+1)/41) \\ Charles R Greathouse IV, Feb 17 2017

A230036 Numbers n such that (39^n + 1)/40 is prime.

Original entry on oeis.org

3, 13, 149, 15377

Offset: 1

Robert Price, Oct 05 2013

All terms are primes.

a(5) > 10^5.

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. A000978 (numbers n such that (2^n + 1)/3 is prime).

Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524.

Do[ p=Prime[n]; If[ PrimeQ[ (39^p + 1)/40 ], Print[p] ], {n, 1, 9592} ]

is(n)=ispseudoprime((39^n+1)/40) \\ Charles R Greathouse IV, Feb 17 2017

A231604 Numbers n such that (42^n + 1)/43 is prime.

Original entry on oeis.org

3, 709, 1637, 17911, 127609, 172663

Offset: 1

Robert Price, Nov 11 2013

The first 5 terms are primes.

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
P. Bourdelais, A Generalized Repunit Conjecture
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. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663.

Do[ p=Prime[n]; If[ PrimeQ[ (42^p + 1)/43 ], Print[p] ], {n, 1, 9592} ]

is(n)=ispseudoprime((42^n+1)/43) \\ Charles R Greathouse IV, Feb 20 2017

a(5)=127609 corresponds to a probable prime discovered by Paul Bourdelais, Jul 02 2018

a(6)=172663 corresponds to a probable prime discovered by Paul Bourdelais, Jul 29 2019

A231865 Numbers n such that (43^n + 1)/44 is prime.

Original entry on oeis.org

5, 7, 19, 251, 277, 383, 503, 3019, 4517, 9967, 29573

Offset: 1

Robert Price, Nov 14 2013

All terms are primes.

a(11) > 10^5.

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. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663, A231604.

Do[ p=Prime[n]; If[ PrimeQ[ (43^p + 1)/44 ], Print[p] ], {n, 1, 9592} ]

is(n)=ispseudoprime((43^n+1)/44) \\ Charles R Greathouse IV, Feb 20 2017

A235683 Numbers n such that (46^n + 1)/47 is prime.

Original entry on oeis.org

7, 23, 59, 71, 107, 223, 331, 2207, 6841, 94841

Offset: 1

Robert Price, Jan 13 2014

All terms up to a(10) are primes.

a(11) > 10^5.

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. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663, A231604, A231865.

Do[ p=Prime[n]; If[ PrimeQ[ (46^p + 1)/47 ], Print[p] ], {n, 1, 9592} ]

is(n)=ispseudoprime((46^n+1)/47) \\ Charles R Greathouse IV, May 22 2017

A237052 Numbers n such that (49^n + 1)/50 is prime.

Original entry on oeis.org

7, 19, 37, 83, 1481, 12527, 20149

Offset: 1

Robert Price, Feb 02 2014

All terms are primes.

a(8) > 10^5.

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. A000978 = numbers n such that (2^n + 1)/3 is prime.

Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663, A231604, A231865, A235683, A236167, A236530.

Do[ p=Prime[n]; If[ PrimeQ[ (49^p + 1)/50 ], Print[p] ], {n, 1, 9592} ]

is(n)=ispseudoprime((49^n+1)/50) \\ Charles R Greathouse IV, Jun 13 2017

Typo in description corrected by Ray Chandler, Feb 20 2017

A236167 Numbers k such that (47^k + 1)/48 is prime.

Original entry on oeis.org

5, 19, 23, 79, 1783, 7681

Offset: 1

Robert Price, Jan 19 2014

a(7) > 10^5.

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. A000978 = numbers k such that (2^k + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663, A231604, A231865, A235683.

Do[ p=Prime[n]; If[ PrimeQ[ (47^p + 1)/48 ], Print[p] ], {n, 1, 9592} ]

is(n)=ispseudoprime((47^n+1)/48) \\ Charles R Greathouse IV, Jun 06 2017

from sympy import isprime
def afind(startat=0, limit=10**9):
  pow47 = 47**startat
  for k in range(startat, limit+1):
    q, r = divmod(pow47+1, 48)
    if r == 0 and isprime(q): print(k, end=", ")
    pow47 *= 47
afind(limit=300) # Michael S. Branicky, May 19 2021

A236530 Numbers n such that (48^n + 1)/49 is prime.

Original entry on oeis.org

5, 17, 131, 84589

Offset: 1

Robert Price, Jan 27 2014

All terms are primes.

a(5) > 10^5.

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. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A007658, A057171, A057172, A057173, A057175, A001562, A057177, A057178, A057179, A057180, A057181, A057182, A057183, A057184, A057185, A057186, A057187, A057188, A057189, A057190, A057191, A071380, A071381, A071382, A084741, A084742, A065507, A126659, A126856, A185240, A229145, A229524, A230036, A229663, A231604, A231865, A235683, A236167.

Do[ p=Prime[n]; If[ PrimeQ[ (48^p + 1)/49 ], Print[p] ], {n, 1, 9592} ]

is(n)=ispseudoprime((48^n+1)/49) \\ Charles R Greathouse IV, Jun 13 2017

Incorrect first term deleted by Robert Price, Feb 21 2014

cp's OEIS Frontend

A229663 Numbers n such that (40^n + 1)/41 is prime.

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A230036 Numbers n such that (39^n + 1)/40 is prime.

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A231604 Numbers n such that (42^n + 1)/43 is prime.

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A231865 Numbers n such that (43^n + 1)/44 is prime.

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A235683 Numbers n such that (46^n + 1)/47 is prime.

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A237052 Numbers n such that (49^n + 1)/50 is prime.

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A236167 Numbers k such that (47^k + 1)/48 is prime.

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A236530 Numbers n such that (48^n + 1)/49 is prime.

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