A097279 - OEIS

%I #3 Mar 30 2012 17:22:33

%S 5,11,23,59,67,83,89,101,107,109,127,163,167,197,229,233,251,283,311,

%T 317,349,421,491,557,577,643,673,683,719,727,761,827,1009,1061,1129,

%U 1163,1193,1231,1327,1373

%N Alternating-harmonic primes.

%C These primes, analogous to the harmonic primes in A092101, divide exactly one term of A058313, the numerators of the alternating harmonic numbers. It can be shown that for prime p > 3, if p = 6k-1, then p divides A058313(4k-1), otherwise if p = 6k+1, then p divides A058313(4k). Much of the analysis by Eswarathasan and Levine applies to alternating harmonic sums.

%D A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.

%t maxPrime=1000; lst={}; Do[p=Prime[n]; cnt=0; s=0; i=1; While[s=s+(-1)^(i-1)/i; If[Mod[Numerator[s], p]==0, cnt++ ]; cnt<2&&i<p^2, i++ ]; If[cnt==1, AppendTo[lst, p]], {n, 3, PrimePi[maxPrime]}]; lst

%K hard,nonn

%O 1,1

%A _T. D. Noe_, Aug 04 2004