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A351682
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Prime numbers p such that the (p-1)-st Bell number B(p-1) is a primitive root modulo p.
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1
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2, 3, 11, 13, 17, 19, 29, 31, 47, 53, 71, 103, 113, 127, 131, 137, 139, 149, 173, 179, 181, 191, 211, 233, 239, 241, 251, 257, 263, 269, 293, 317, 347, 367, 379, 401, 431, 439, 449, 461, 503, 509, 523, 541, 557, 587, 607, 617, 619, 647, 653, 683, 691, 733, 743, 761, 773, 797, 821, 823, 827, 853, 859, 881, 919, 929
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OFFSET
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1,1
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COMMENTS
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Heuristically, the density of the sequence in the primes should approach Artin's constant: 0.3739558136...
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LINKS
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EXAMPLE
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For n = 2 one has a(2) = 3 since B(2) = 2 is a primitive root modulo 3.
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MAPLE
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filter:= proc(p) local b;
b:= combinat:-bell(p-1);
numtheory:-order(b, p) = p-1
end proc:
select(filter, [seq(ithprime(i), i=1..200)]); # Robert Israel, May 04 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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