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A187026 Least m such that prime(n) divides (prime(m) + prime(m+1))/2.

%I A187026 #25 Nov 14 2014 09:58:57
%S A187026 2,3,6,8,25,9,11,21,19,69,24,29,46,23,60,115,51,111,32,82,129,185,132,
%T A187026 71,106,155,63,116,84,203,54,77,58,145,108,87,289,93,67,443,254,460,
%U A187026 292,76,350,300,447,86,397,124,284,808,128,335,136
%N A187026 Least m such that prime(n) divides (prime(m) + prime(m+1))/2.
%H A187026 Alois P. Heinz, <a href="/A187026/b187026.txt">Table of n, a(n) for n = 1..5000</a>
%e A187026 a(1) = 2 because prime(1)=2 divides (prime(2)+prime(3))/2 = (3+5)/2 = 4.
%p A187026 a:= proc(n) local m, pn; pn:= ithprime(n);
%p A187026       for m from n+1 while not irem((ithprime(m)+ithprime(m+1))/2, pn)=0
%p A187026       do od; m
%p A187026     end:
%p A187026 seq(a(n), n=1..80);  # _Alois P. Heinz_, Mar 02 2011
%t A187026 leastM[n_]:=Module[{m=1},While[!Divisible[(Prime[m]+Prime[m+1])/2,n],m++];m]; leastM/@Prime[Range[60]] (* _Harvey P. Dale_, Mar 04 2011 *)
%Y A187026 Cf. A000040, A024675.
%K A187026 nonn
%O A187026 1,1
%A A187026 _Vladimir Shevelev_, Mar 02 2011