A236167
Numbers k such that (47^k + 1)/48 is prime.
Original entry on oeis.org
5, 19, 23, 79, 1783, 7681
Offset: 1
- 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
A185230
Numbers n such that (33^n + 1)/34 is prime.
Original entry on oeis.org
5, 67, 157, 12211, 313553
Offset: 1
- 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. Cf.
A084741,
A084742,
A065507,
A126659,
A126856.
-
Do[ p=Prime[n]; If[ PrimeQ[ (33^p + 1)/34 ], Print[p] ], {n, 1, 9592} ]
-
is(n)=ispseudoprime((33^n+1)/34) \\ Charles R Greathouse IV, Jun 13 2017
A236530
Numbers n such that (48^n + 1)/49 is prime.
Original entry on oeis.org
5, 17, 131, 84589
Offset: 1
- 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
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