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A168069 a(n) is the index k of the smallest k-th prime p(k) with f(k,n):=(p(k) + p(k+1))/n an integer (n = 1,2,3,...)

%I A168069 #1 Jun 01 2010 03:00:00
%S A168069 1,2,3,2,1,3,8,2,4,6,13,3,9,8,6,16,11,4,21,10,8,13,19,5,14,9,22,16,69,
%T A168069 6,24,18,25,11,7,29,21,12,17
%N A168069 a(n) is the index k of the smallest k-th prime p(k) with f(k,n):=(p(k) + p(k+1))/n an integer (n = 1,2,3,...)
%C A168069 (1) EVERY natural k appears in the sequence, some more than once
%C A168069 (2) Theoretical interest for cases (I) a(n) < n, (II) a(n) = n, (I) a(n) > n
%C A168069 (3) Note cases n=1, 3, 16, ... with a(n) = n
%D A168069 Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
%D A168069 Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
%e A168069 (1) p(1)+p(2)=2+3=1 x 5 gives a(1)=a(5)=1
%e A168069 (2) p(3)+p(4)=5+7=2^2 x 3 gives a(3)=a(6)=a(12)=3, but a(2)=2 < 3, because p(2)+p(2)=2 x 2^2
%e A168069 (3) p(16)+p(17)=53+59=2^4 x 7=16 x 7 gives a(16)=16
%e A168069 (4) p(69)+p(70)=347+349=2^3 x 3 x 29 gives a(29)=69
%Y A168069 A000040 The prime numbers
%Y A168069 A167790
%K A168069 nonn
%O A168069 1,2
%A A168069 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 18 2009