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A188133
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Primes p such that 10p+1 divides 2^p-1.
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4
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43, 487, 547, 571, 883, 1459, 1663, 1723, 2539, 3319, 3511, 4903, 5107, 5431, 6199, 6367, 8011, 8599, 9007, 9391, 9511, 10111, 11119, 11959, 12379, 12703, 13291, 13339, 13999, 14083, 14551, 14767, 15187, 15319, 15859, 15991, 16183, 16603, 16747, 17659, 18427, 19699
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OFFSET
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1,1
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COMMENTS
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It is known that divisors of M(p)=2^p-1 are of the form 2kp+1. For k=1, these are the Lucasian primes A002515, for k=2 there are no such divisors, for k=3 these divisors are listed in A188130 and for k=4 in A122095.
The equivalent sequence of prime indices is 14, 93, 101, 105, 153, 232, 261, 269, ....
If k == 2 (mod 4), there are no such divisors in general and here there are no smaller k's than k = 5. - Karl-Heinz Hofmann, Jan 27 2022
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[2*10^4], PrimeQ[#] && PowerMod[2, #, 10# + 1] == 1 &] (* Amiram Eldar, Nov 13 2019 *)
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PROG
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(PARI) forprime(p=1, 1e5, Mod(2, p*10+1)^p-1 | print1(p", "))
(Python) from sympy import sieve
print([p for p in sieve[1:10000] if pow(2, p, 10*p+1) == 1])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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