A134694 a(0) = 2; a(n) = least prime p such that p >= a(n-1) + 2^n.

2, 5, 11, 19, 37, 71, 137, 269, 541, 1061, 2087, 4139, 8237, 16433, 32831, 65599, 131143, 262217, 524369, 1048661, 2097257, 4194409, 8388733, 16777381, 33554639, 67109071, 134217943, 268435697, 536871157, 1073742073, 2147483929

Offset: 0

Author

Walter Carlini, Jan 27 2008

Keywords

• easy
• nonn

Comments

Primes separated by at least successive powers of 2.

Examples

			a(0) = 2 (by definition).
a(1) = 5 because 5 is the least prime >= 4 = 2 + 2^1.
a(2) = 11 because 11 is the least prime >= 9 = 5 + 2^2.
a(3) = 19 because 19 is the least prime >= 19 = 11 + 2^3.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000040.

Programs

Mathematica

a = {2}; Do[i = a[[ -1]]+2^n; While[ !PrimeQ[i], i++ ]; AppendTo[a, i], {n,1,50}]; a (* Stefan Steinerberger, Jan 28 2008 *)
nxt[{n_,a_}]:={n+1,NextPrime[a+2^(n+1)-1]}; NestList[nxt,{0,2},30][[All,2]] (* Harvey P. Dale, Jan 04 2017 *)

Extensions

More terms from Stefan Steinerberger, Jan 28 2008