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 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. 0

%I

%S 1,3,5,5,11,19,13,19,23,39,19,37,37,37,53,53,47,47,31,61,61,71,53,53,

%T 89,73,47,89,83,91,127,89,101,127,167,109,73,145,199,137,127,193,101,

%U 109,163,149,137,241,211,163,251,281,151,265,181,339,269,229,209,187

%N 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletsTheorem.html">Dirichlet's Theorem.</a>

%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>

%e a(20)=61, as 20+k*61 is not prime for k<=6: 20+1*61=3^4,

%e 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 and 20+7*61=447>20^2; and for coprimes that are less than 61 there exist

%e primes <= 20^2: 20+3*1=23, 20+1*3=23, 20+3*7=41, 20+1*9=29, 20+1*11=31,

%e 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 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 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 or 20+1*59=79.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jan 03 2004

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Last modified June 17 19:57 EDT 2021. Contains 345085 sequences. (Running on oeis4.)