login
A308177
Numbers x congruent to 1 mod 6 such that for all k >= 1 the values (x*4^k - 1)/3 are composite integers.
2
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
OFFSET
1,1
COMMENTS
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
REFERENCES
N. J. A. Sloane and many others, Sequence Fans Mailing List, starting May 26 2019.
LINKS
SeqFan Discussion List, Question from Harvey Dale about A233552, protocol of thread, May 29 2019.
CROSSREFS
Cf. A233551.
Sequence in context: A109861 A348754 A106564 * A104777 A289829 A358060
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
Corrected by Jean-Paul Allouche, Harvey P. Dale, M. F. Hasler, Robert Israel, Hugo Pfoertner, David Radcliffe, Don Reble, Andrew Weimholt, and other Sequence Fans, May 26 2019 - May 28 2019
Extended by showing that (3919*4^172171-1)/3 and (5461*4^94937-1)/3 are prime by Hugo Pfoertner, May 30 2019
STATUS
approved