A288160 a(n) = smallest k such that (6*k*n-3)*2^n-1 is prime, or 0 if no such prime exists.

1, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 4, 6, 6, 0, 15, 2, 8, 3, 1, 9, 4, 3, 14, 1, 0, 3, 0, 1, 2, 1, 3, 4, 25, 0, 1, 24, 2, 17, 22, 2, 4, 16, 2, 13, 9, 17, 17, 0, 10, 17, 3, 6, 34, 0, 1, 69, 5, 26, 8, 4, 3, 3, 8, 16, 19, 3, 5, 5, 0, 18, 8, 75, 5, 0, 1, 0, 37, 19, 14, 85, 4, 4, 47

Offset

1,2

Comments

For some n (6*k*n-3)*2^n-1 is composite for any k.

For n=15+20*j, n=7+21*j, n=77+110*j, n=26+156*j, n=266+342*j, n=261+812*j, n=2368+1332*j, n=477+2756*j, n=2183+3422*j and more others (6*k*n-3)*2^n-1 is always composite for any k and any j.

For n=4390+187892*j, (6*k*n-3)*2^n-1 is always divisible by one of the 82 primes between 5 and 443, 4390=10*439 and 187892=438*439.

For n=6152+596744*j, (6*k*n-3)*2^n-1 is always divisible by one of the 134 primes between 3 and 773, 6152=8*769 and 596744=768*769.

For n=11*1229+1228*1229*j, (6*n*k-3)*2^n-1 is always divisible by one of the 199 primes between 3 and 1231 except 11.

For n=27*1399+1398*1399*j, (6*n*k-3)*2^n-1 is always divisible by one of the 220 primes between 3 and 1409.

For n=5*11*1619+1618*1619*j, (6*n*k-3)*2^n-1 is always divisible by one of the 253 primes between 5 and 1621 except 11.

Links

Pierre CAMI, Table of n, a(n) for n = 1..9000

Crossrefs

Cf. A285808.

Sequence in context: A160096 A029446 A358479 * A275332 A029442 A125917

Adjacent sequences: A288157 A288158 A288159 * A288161 A288162 A288163

Keyword

nonn

Author

Pierre CAMI, Jun 19 2017

Status

approved