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} ]
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is(n)=ispseudoprime((48^n+1)/49) \\ Charles R Greathouse IV, Jun 13 2017
A309358
Numbers k such that 10^k + 1 is a semiprime.
Original entry on oeis.org
4, 5, 6, 7, 8, 19, 31, 53, 67, 293, 586, 641, 922, 2137, 3011
Offset: 1
a(1) = 4 because 10^4 + 1 = 10001 = 73*137.
-
IsSemiprime:=func; [n: n in [2..200] | IsSemiprime(s) where s is 10^n+1]; // Vincenzo Librandi, Jul 31 2019
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Select[Range[200], Plus@@Last/@FactorInteger[10^# + 1] == 2 &] (* Vincenzo Librandi, Jul 31 2019 *)
A216531
Numbers n such that (10^n + 1)/11 is prime and can be written in the form a^2 + 7*b^2.
Original entry on oeis.org
7, 19, 31, 67, 2137, 268207
Offset: 1
A216533
Numbers n such that (10^n + 1)/11 is prime, but cannot be written in the form a^2 + 7*b^2.
Original entry on oeis.org
5, 53, 293, 641, 3011
Offset: 1
A294396
Numbers k such that 12*10^k + 1 is prime.
Original entry on oeis.org
0, 2, 38, 80, 9230, 25598, 39500
Offset: 1
13 and 1201 are prime, so 0 and 2 are the initial values.
Cf.
A001562,
A096507,
A056797,
A056807,
A056806,
A102940,
A056805,
A056804,
A096508,
A102975,
A289051,
A099017,
A295325,
A273002,
A102945,
A282456,
A267420.
Cf.
A062339 (primes with digit sum 4).
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ParallelMap[ If[ PrimeQ[12*10^# +1], #, Nothing] &, 2 + 6Range@ 4500] (* Robert G. Wilson v, Feb 13 2018 *)
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isok(k) = isprime(12*10^k + 1); \\ Altug Alkan, Mar 04 2018
A328660
Numbers k such that (10^k + 7^k)/17 is prime.
Original entry on oeis.org
3, 5, 11, 19, 1259, 1399, 2539, 2843, 5857, 10589
Offset: 1
-
[p: p in PrimesUpTo(1000) | IsPrime((10^p+7^p) div 17)]; // Modified by Jinyuan Wang, Jan 22 2020
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Select[Table[Prime[n], {n, 500}], PrimeQ[(10^#+7^#)/17] &] (* Modified by Jinyuan Wang, Jan 22 2020 *)
-
forprime(k=3, 10000, if(isprime((10^k+7^k)/17), print1(k, ", ")))
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