A135833 Number of Section I primes between 2^n and 2^(n+1). See A135832.

1, 2, 2, 4, 5, 7, 9, 13, 18, 21, 28, 43, 56, 62, 72, 94, 133, 142, 187, 241, 313, 376, 436, 517, 709, 858, 982, 1271, 1561, 1814, 2192, 2658, 3184, 3853, 4601, 5648, 6881, 8009, 9535, 11651, 13712, 16325, 19381, 23323, 27097, 31782, 37924, 44673, 52695, 62147

Offset: 1

Author

T. D. Noe, Nov 30 2007

Keywords

• nonn

Comments

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.

Examples

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

Links

• T. D. Noe, Computing Numbers in Section I of the Totient Iteration

Crossrefs

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

Programs

Mathematica

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 *)

Extensions

More terms from T. D. Noe, Aug 04 2008

Extension. T. D. Noe, Nov 18 2008