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85, 49, 133, 81, 363, 705, 881, 1023, 417, 653, 773, 1229, 1985, 273, 275, 585, 1365, 2505, 3861, 129, 289, 719, 2069, 2393, 3113, 4609, 5549, 5555, 5789, 6299, 7517, 7649, 321, 2321, 2337, 3567, 6617, 6993, 9377, 12957, 13737, 14505, 15033, 15225, 15237, 385, 2177, 2565, 7097, 8273, 8897
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OFFSET
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1,1
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COMMENTS
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This sequence contains the distances from pseudoprime numbers (A001567) to the next smaller number of the form 2^n. Conjecture: It seems that these distances do not take all possible values. So, if we know that a certain distance does not appear with pseudoprime numbers, we are able to calculate these numbers using Fermat's little theorem and we know for sure that they are primes.
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LINKS
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EXAMPLE
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There are no pseudoprimes detected by Fermat's little theorem for 2^k+m with m = {3,5,7,...,47} up to k = 10000 (checked using the Pari function ispseudoprime(k)). When this sequence is ordered for the first 10^5 pseudoprimes, the following first terms (up to 1000) result: 1, 49, 81, 85, 129, 133, 273, 275, 289, 321, 363, 385, 417, 585, 653, 705, 719, 773, 881.
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MATHEMATICA
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Map[# - 2^Floor@ Log2@ # &, Select[Range[3, 10^5, 2], And[! PrimeQ[#], PowerMod[2, (# - 1), #] == 1] &]] (* Michael De Vlieger, Nov 26 2017 *)
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PROG
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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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