A214934 Numbers R(k) such that R(k) >= 2k log R(k), where R(k) = A104272(k) is the k-th Ramanujan prime.

2, 11, 17, 29, 41, 47, 59, 97, 127, 149, 151, 167, 179, 227, 229, 233, 347, 367, 401, 409, 569, 571, 587, 593, 937, 1423, 1427, 2237, 2617, 2657, 2659, 3251

Offset: 1

Author

John W. Nicholson, Jan 03 2013

Keywords

• nonn
• fini
• full

Comments

For all R(k) > 3251, or all k > 201, R(k) < 2k log R(k). - John W. Nicholson, Nov 05 2016

Links

• C. Axler, On generalized Ramanujan primes, arXiv preprint arXiv:1401.7179 [math.NT], 2014.

Programs

Mathematica

nn = 201; R = Table[0, {nn}]; s = 0; Do[ If[ PrimeQ[k], s++]; If[ PrimeQ[k/2], s--]; If[s < nn, R[[s +1]] = k], {k, Prime[3nn]}]; R = R +1; R[[#]] & /@ Select[ Range@ nn, R[[#]] >= 2#*Log[R[[#]]] &] (* Robert G. Wilson v, Nov 05 2016 after T. D. Noe in A104272 *)

PARI

\\With RR[i] a list of Ramanujan primes in A104272.
\\Program also gives the index i of A104272.
n=0;for(i=1,10^6,if(RR[i]/(2*i)>=log(RR[i]), print(n++," "i," ",primepi(RR[i])," ",RR[i])))