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A103622 Smallest arithmetic mean of n distinct primes.

%I A103622 #10 Mar 06 2018 03:03:32
%S A103622 2,4,4,7,6,11,10,13,12,17,16,21,20,24,24,29,26,32,32,36,36,41,38,45,
%T A103622 44,49,48,53,52,58,58,63,62,68,66,72,70,77,76,83,80,87,86,92,90,97,96,
%U A103622 102,100,108,106,113,110,118,116,123,122,129,126,133,132,139,138,145,142
%N A103622 Smallest arithmetic mean of n distinct primes.
%C A103622 Often a(2n+1) = a(2n) - 1. - _Robert G. Wilson v_, Jan 19 2007
%e A103622 a(1)=2 because (2)/1=2,
%e A103622 a(2)=4 because (3+5)/2=4,
%e A103622 a(3)=4 because (2+3+7)/3=4,
%e A103622 a(4)=7 because (3+5+7+13)/4=7,
%e A103622 a(5)=6 because (2+3+5+7+13)/5=6,
%e A103622 a(6)=11 because (3+5+7+11+17+23)/6=11,
%e A103622 a(7)=10 because (2+3+5+7+11+13+29)/7=10,
%e A103622 a(8)=13 because (3+5+7+11+13+17+19+29)/8=13,
%e A103622 a(9)=12 because (2+3+5+7+11+13+17+19+31)/9=12,
%e A103622 a(10)=17 because (3+5+7+11+13+17+19+23+29+43)/10=17, etc.
%t A103622 f[n_] := Block[{k = 1, lst = Prime@ Range[ If[ OddQ@ n, 1, 2], n + 3]}, While[ Mod[Plus @@ Flatten@Subsets[lst, {n}, {k}], n] != 0, k++ ]; (Plus @@ Flatten@ Subsets[lst, {n}, {k}])/n]; Array[f, 65] (* _Robert G. Wilson v_, Jan 19 2007 *)
%Y A103622 Cf. A072701.
%K A103622 easy,nonn
%O A103622 1,1
%A A103622 _Giovanni Teofilatto_, Mar 25 2005
%E A103622 Edited, corrected and extended by _Robert G. Wilson v_, Jan 19 2007