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Number of Ramanujan primes R_k such that 2^(n-1) < R_k <= 2^n.
3

%I #34 May 05 2017 19:36:52

%S 0,1,0,0,1,2,3,6,10,19,33,62,118,208,409,740,1418,2676,5043,9638,

%T 18248,34949,66752,127880,245489,472113,908302,1751624,3381546,

%U 6534616,12645372,24490255,47485123,92152929,178987716,347943866,676925069,1317911597,2567659990,5005877954,9765539069,19062301793,37230980158,72756216207,142253989491,278275735952,544621563320,1066382258001

%N Number of Ramanujan primes R_k such that 2^(n-1) < R_k <= 2^n.

%H Dana Jacobsen, <a href="/A190501/b190501.txt">Table of n, a(n) for n = 0..56</a>

%o (PARI) \\ With RR[.] is a list of A104272(.). The output of this program is (for n>=1) n, A190502(n), and RR[a(n)], a(n).

%o j=0;while(2^j<RR[10^8],{n=1;while(RR[n]<=2^j,n++);pn=n-1;if(n<=1,print(j," ",0," none"),print(j," ",pn," ",RR[pn]," ",pn-pn2));pn2=pn;j++});

%o (Perl) use ntheory ":all"; say "$_ ",ramanujan_prime_count(1 << $_) - ramanujan_prime_count(1 << ($_-1)) for 0..56; # _Dana Jacobsen_, May 05 2017

%Y Cf. A007053, A036378, A104272, A190502.

%K nonn

%O 0,6

%A _John W. Nicholson_, May 11 2011

%E Extended by _T. D. Noe_, May 11 2011

%E Modified the name as to match offset to A190502 and added leading term, _John W. Nicholson_, May 12 2011

%E Extended to n = 32 by _John W. Nicholson_, Dec 01 2012

%E Extended to n = 47, using A190502 data, by _John W. Nicholson_, Jan 31 2016