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
KEYWORD
nonn
AUTHOR
Pierre CAMI, Jun 19 2017
STATUS
approved