A308177 Numbers x congruent to 1 mod 6 such that for all k >= 1 the values (x*4^k - 1)/3 are composite integers.

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

Table of n, a(n) for n=1..36.

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

Adjacent sequences: A308174 A308175 A308176 * A308178 A308179 A308180

Keyword

nonn,more

Author

Arkadiusz Wesolowski, Dec 12 2013

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