Search: id:A089167
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%I A089167
%S A089167 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,
%T A089167 73,47,89,83,91,127,89,101,127,167,109,73,145,199,137,127,193,101,109,
%U A089167 163,149,137,241,211,163,251,281,151,265,181,339,269,229,209,187
%N 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.
%H A089167 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DirichletsTheorem.html">Dirichlet's Theorem.</a>
%H A089167 <a href="Sindx_Pri.html#primes_AP">Index entries for sequences related 
               to primes in arithmetic progressions</a>
%e A089167 a(20)=61, as 20+k*61 is not prime for k<=6: 20+1*61=3^4,
%e A089167 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,
%e A089167 and 20+7*61=447>20^2; and for coprimes that are less than 61 there exist
%e A089167 primes <= 20^2: 20+3*1=23, 20+1*3=23, 20+3*7=41, 20+1*9=29, 20+1*11=31,
%e A089167 20+3*13=59, 20+1*17=37, 20+9*19=191, 20+1*21=41, 20+1*23=43, 20+1*27=47,
%e A089167 20+3*29=107, 20+3*31=113, 20+1*33=53, 20+3*37=131, 20+1*39=59, 20+1*41=61,
%e A089167 20+3*43=149, 20+1*47=67, 20+3*49=167, 20+1*51=71, 20+1*53=73, 20+3*57=191,
%e A089167 or 20+1*59=79.
%Y A089167 Sequence in context: A098971 A093572 A118132 this_sequence A028265 A084041 
               A028254
%Y A089167 Adjacent sequences: A089164 A089165 A089166 this_sequence A089168 A089169 
               A089170
%K A089167 nonn
%O A089167 1,2
%A A089167 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 03 2004

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