A235213 - OEIS

%I #21 Jan 24 2014 11:21:41

%S 2,3,5,7,11,17,23,31,47,73,107,157,233,347,509,743,1103,1627,2399,

%T 3541,5227,7717,11383,16811,24799,36599,54011,79699,117619,173573,

%U 256163,378041,557891,823309,1215017,1793081,2646167,3905059,5762969,8504759,12550991,18522269

%N Nearest prime to (2^(e^-gamma))^n, where gamma is the Euler-Mascheroni constant.

%C The nearest integer to (2^(e^-gamma))^n is very close to A018133.

%H Eric W. Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WagstaffsConjecture.html">Wagstaff's Conjecture</a>

%H Eric W. Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EberhartsConjecture.html">Eberhart's Conjecture</a>

%F Nearest prime to (2^(e^-A001620))^n = (2^A080130)^n.

%t f[n_] := Block[{a = (2^Exp[-EulerGamma])^n}, Nearest[{NextPrime[a], NextPrime[a, -1]}, a][[1]]]; Array[f, 42, 2]

%o (PARI) a(n)=my(t=2^(exp(Euler)*n),mn=precprime(t),mx=nextprime(t)); if(mx-t<t-mn, mx, mn) \\ _Charles R Greathouse IV_, Jan 04 2014

%Y Cf. A000043, A001620, A080130.

%K nonn,easy

%O 2,1

%A _Robert G. Wilson v_, Jan 04 2014