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 A188133 Primes p such that 10p+1 divides 2^p-1. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA {p = A000040(i): 10*p+1 | A001348(i)}. - R. J. Mathar, Mar 21 2011 MATHEMATICA Select[Range[2*10^4], PrimeQ[#] && PowerMod[2, #, 10# + 1] == 1 &] (* Amiram Eldar, Nov 13 2019 *) PROG (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]) # Karl-Heinz Hofmann, Jan 27 2022 CROSSREFS Cf. A002515 (k = 1), A188130 (k = 3), A122095 (k = 4), A350702 (k = 7). Cf. A001348, A000040. Sequence in context: A247966 A248206 A140849 * A194784 A184153 A184145 Adjacent sequences: A188130 A188131 A188132 * A188134 A188135 A188136 KEYWORD nonn AUTHOR M. F. Hasler, Mar 21 2011 STATUS approved

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Last modified June 8 13:50 EDT 2023. Contains 363165 sequences. (Running on oeis4.)