A135833 - OEIS

%I #5 Jan 29 2014 17:17:31

%S 1,2,2,4,5,7,9,13,18,21,28,43,56,62,72,94,133,142,187,241,313,376,436,

%T 517,709,858,982,1271,1561,1814,2192,2658,3184,3853,4601,5648,6881,

%U 8009,9535,11651,13712,16325,19381,23323,27097,31782,37924,44673,52695,62147

%N Number of Section I primes between 2^n and 2^(n+1). See A135832.

%C Comparing these numbers with A036378, the number of primes between 2^n and 2^(n+1), leads one to conjecture that the density of Section I primes is 0.

%H T. D. Noe, <a href="http://www.sspectra.com/math/IteratedPhi2.pdf">Computing Numbers in Section I of the Totient Iteration</a>

%e 3; 5, 7; 11, 13; 17, 23, 29, 31; 41, 47, 53, 59, 61; 83,...

%t class[ n_ ] := Length[ NestWhileList[ EulerPhi,n,#>2& ] ]-1; k=2; Table[ cnt=0; While[ p=Prime[ k ]; p<2^(n+1), If[ class[ p ]==n, cnt++ ]; k++ ]; cnt, {n,20} ] (* _T. D. Noe_, Aug 04 2008 *)

%Y Cf. A092878 (number of odd numbers in Section I).

%K nonn

%O 1,2

%A _T. D. Noe_, Nov 30 2007

%E More terms from _T. D. Noe_, Aug 04 2008

%E Extension. _T. D. Noe_, Nov 18 2008