A089167 Smallest number m that is coprime to n and such that the arithmetic progression (n+k*m:k>0) contains no primes for values not greater than n^2; a(1)=1.

1, 3, 5, 5, 11, 19, 13, 19, 23, 39, 19, 37, 37, 37, 53, 53, 47, 47, 31, 61, 61, 71, 53, 53, 89, 73, 47, 89, 83, 91, 127, 89, 101, 127, 167, 109, 73, 145, 199, 137, 127, 193, 101, 109, 163, 149, 137, 241, 211, 163, 251, 281, 151, 265, 181, 339, 269, 229, 209, 187

Offset

1,2

Links

Table of n, a(n) for n=1..60.

Eric Weisstein's World of Mathematics, Dirichlet's Theorem.

Index entries for sequences related to primes in arithmetic progressions

Example

a(20)=61, as 20+k*61 is not prime for k<=6: 20+1*61=3^4,
20+2*61=71*2, 20+3*61=29*7, 20+4*61=11*3*2^3, 20+5*61=13*5^2, 20+6*61=193*2,
and 20+7*61=447>20^2; and for coprimes that are less than 61 there exist
primes <= 20^2: 20+3*1=23, 20+1*3=23, 20+3*7=41, 20+1*9=29, 20+1*11=31,
20+3*13=59, 20+1*17=37, 20+9*19=191, 20+1*21=41, 20+1*23=43, 20+1*27=47,
20+3*29=107, 20+3*31=113, 20+1*33=53, 20+3*37=131, 20+1*39=59, 20+1*41=61,
20+3*43=149, 20+1*47=67, 20+3*49=167, 20+1*51=71, 20+1*53=73, 20+3*57=191,
or 20+1*59=79.

Crossrefs

Sequence in context: A240731 A266505 A118132 * A188345 A349204 A028265

Adjacent sequences: A089164 A089165 A089166 * A089168 A089169 A089170

Keyword

nonn

Author

Reinhard Zumkeller, Jan 03 2004

Status

approved