A168069 - OEIS

%I #1 Jun 01 2010 03:00:00

%S 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 6,24,18,25,11,7,29,21,12,17

%N 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 (1) EVERY natural k appears in the sequence, some more than once

%C (2) Theoretical interest for cases (I) a(n) < n, (II) a(n) = n, (I) a(n) > n

%C (3) Note cases n=1, 3, 16, ... with a(n) = n

%D Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980

%D Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005

%e (1) p(1)+p(2)=2+3=1 x 5 gives a(1)=a(5)=1

%e (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 (3) p(16)+p(17)=53+59=2^4 x 7=16 x 7 gives a(16)=16

%e (4) p(69)+p(70)=347+349=2^3 x 3 x 29 gives a(29)=69

%Y A000040 The prime numbers

%Y A167790

%K nonn

%O 1,2

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 18 2009