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A308177
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Numbers x congruent to 1 mod 6 such that for all k >= 1 the values (x*4^k - 1)/3 are composite integers.
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2
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25, 49, 121, 169, 289, 361, 529, 625, 841, 919, 961, 1225, 1369, 1681, 1849, 2209, 2401, 2419, 2629, 2809, 3025, 3301, 3481, 3721, 4225, 4489, 5041, 5209, 5329, 5539, 5581, 5929, 6241, 6421, 6889, 7225
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OFFSET
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1,1
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COMMENTS
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The sequence contains all 1-mod-6 squares except 1 as well as other values. (For example, 2167411, whose covering set moduli divide 4^24-1.)
The least unknown value (2019 May 30) is 7309 with (7309*4^k - 1)/3 shown to be composite for all k < 120000. - Hugo Pfoertner, May 30 2019
Don Reble observed that the erroneous version A233552 is the list of n which can be proved to have (n*4^k-1)/3 composite for all k using the divisors of 4^12-1 as covering set of moduli. - M. F. Hasler, May 28 2019
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REFERENCES
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N. J. A. Sloane and many others, Sequence Fans Mailing List, starting May 26 2019.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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Extended by showing that (3919*4^172171-1)/3 and (5461*4^94937-1)/3 are prime by Hugo Pfoertner, May 30 2019
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STATUS
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approved
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