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A214934 Numbers R(k) such that R(k) >= 2k log R(k), where R(k) = A104272(k) is the k-th Ramanujan prime. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..32.

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

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 *)

PROG

(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])))

CROSSREFS

Sequence in context: A164368 A194658 A104272 * A233866 A117155 A186782

Adjacent sequences:  A214931 A214932 A214933 * A214935 A214936 A214937

KEYWORD

nonn,fini,full

AUTHOR

John W. Nicholson, Jan 03 2013

STATUS

approved

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Last modified August 15 12:14 EDT 2020. Contains 336494 sequences. (Running on oeis4.)