|
COMMENT
|
I conjecture that a(n) for every n greater than 1 exist and is less than n^2. I have defined for each n (n>1), a sequence {fni(m)} of nonnegative integers (probably infinite) such that fni(m) is the m-th nonnegative integer such that fi(n,fni(m)) is prime number. For example : f2i=A032702 f3i: 5,8,11,20,22,23,28,34,37,38,41,43,44,52,53,56,59,71,74,77,79, 82,83,86,88,94,110,128,133,134,137,140,152,154... f4i: 14,15,23,25,37,39,44,54,55,70,79,88,90,98,102,118,123,134,136,143 144,151,174,182,202,209,215,226,230,232,245,254,... f5i: 5,17,20,23,25,28,29,56,58,71,77,109,130,140,154, 160,167,196,206,233,244,245... f6i: 5,8,14,44,70,73,79,80,91,107,121,170,191,209,238, 260,269,280,293,302,308,314,... f7i: 9,15,17,41,52,80,89,92,109,128,152,162,169,176,200, 217,230,251,257,272,280,286,... . . f82i: 1404,1750,1762,1959,2000,... (cf. Prime bylisting www.primepuzzles.net) . . . By this definition a(n)=fni(1) for n>1.
|
