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

0,1

Comments

Primes separated by at least successive powers of 2.

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000040.

Sequence in context: A040105 A319859 A156768 * A121606 A166164 A097008

Adjacent sequences: A134691 A134692 A134693 * A134695 A134696 A134697

Keyword

easy,nonn

Author

Walter Carlini, Jan 27 2008

Extensions

More terms from Stefan Steinerberger, Jan 28 2008

Status

approved