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

1,2

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.

Links

Table of n, a(n) for n=1..50.

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A206557 A240508 A174068 * A137200 A026930 A211862

Adjacent sequences: A135830 A135831 A135832 * A135834 A135835 A135836

Keyword

nonn

Author

T. D. Noe, Nov 30 2007

Extensions

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

Extension. T. D. Noe, Nov 18 2008

Status

approved