A214120 Number of Proth primes < 2^n.

0, 1, 2, 3, 4, 5, 7, 9, 12, 17, 21, 27, 33, 50, 62, 84, 110, 148, 182, 253, 327, 467, 610, 855, 1097, 1548, 1999, 2849, 3648, 5231, 6761, 9781, 12631, 18293, 23770, 34407, 44704, 64911, 84734, 122742, 160055, 233124, 303882, 442949, 578588, 843890, 1103500

Offset: 1

Author

Arkadiusz Wesolowski, Jul 04 2012

Keywords

• nonn

Examples

			a(5) = 4 since first 4 Proth primes are 3, 5, 13, 17 all < 2^5.
		

Links

• Chris Caldwell, The Top 20 Proth Primes
• Chris Caldwell, The Prime Glossary, Proth prime

Crossrefs

Cf. A080076.

Programs

Mathematica

lst2 = {}; r = 47; lst1 = Union[Flatten@Table[Select[1 + 2^k*Range[1, 2^Min[k, r - k], 2], # < 2^r && PrimeQ[#] &], {k, r}]]; Do[AppendTo[lst2, Length@Select[lst1, # < 2^n &]], {n, r}]; lst2

PARI

a(n)=my(c=0); for(m=1, n-1, k=1; until(k>2^m, p=k*2^m+1; if(p>2^n, break); if(isprime(p), c++); k=k+2)); c; \\ Arkadiusz Wesolowski, Mar 14 2014