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,...)

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

Offset: 1

Author

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

Keywords

• nonn

Comments

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

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

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

Examples

			(1) p(1)+p(2)=2+3=1 x 5 gives a(1)=a(5)=1
(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
(3) p(16)+p(17)=53+59=2^4 x 7=16 x 7 gives a(16)=16
(4) p(69)+p(70)=347+349=2^3 x 3 x 29 gives a(29)=69
		

References

• Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
• Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005

Crossrefs

A000040 The prime numbers

A167790