A185191 a(n) = 2^n - second largest prime less than 2^n.

2, 3, 5, 3, 5, 15, 15, 9, 5, 19, 5, 13, 15, 49, 17, 9, 11, 19, 5, 19, 17, 21, 17, 49, 27, 79, 89, 33, 41, 19, 17, 25, 77, 49, 17, 31, 87, 19, 167, 31, 17, 67, 117, 69, 57, 127, 65, 111, 35, 139, 143, 145, 53, 67, 27, 25, 57, 99, 107, 31, 87, 165, 83

Offset: 2

Author

Washington Bomfim, Jan 23 2012

Keywords

• nonn

Examples

			a(2)=2 because precprime(4)=3, and precprime(2)=2.
		

References

• D. E. Knuth, The Art of Computer Programming Second Edition. Vol. 2, Seminumerical Algorithms. Chapter 4.5.4 Factoring into Primes, Table 1, Page 390, Addison-Wesley, Reading, MA, 1981.

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A013603.

Programs

Mathematica

Table[2^n - NextPrime[2^n, -2], {n, 2, 64}] (* T. D. Noe, Jan 24 2012 *)
#-NextPrime[#,-2]&/@(2^Range[2,70]) (* Harvey P. Dale, Mar 29 2025 *)

Formula

a(n) = 2^n - precprime(precprime(2^n)-1)