A190501 Number of Ramanujan primes R_k such that 2^(n-1) < R_k <= 2^n.

0, 1, 0, 0, 1, 2, 3, 6, 10, 19, 33, 62, 118, 208, 409, 740, 1418, 2676, 5043, 9638, 18248, 34949, 66752, 127880, 245489, 472113, 908302, 1751624, 3381546, 6534616, 12645372, 24490255, 47485123, 92152929, 178987716, 347943866, 676925069, 1317911597, 2567659990, 5005877954, 9765539069, 19062301793, 37230980158, 72756216207, 142253989491, 278275735952, 544621563320, 1066382258001

Offset

0,6

Links

Dana Jacobsen, Table of n, a(n) for n = 0..56

Prog

(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).
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++});
(Perl) use ntheory ":all"; say "$_ ", ramanujan_prime_count(1 << $_) - ramanujan_prime_count(1 << ($_-1)) for 0..56; # Dana Jacobsen, May 05 2017

Crossrefs

Cf. A007053, A036378, A104272, A190502.

Sequence in context: A191519 A165920 A274160 * A026021 A374690 A291875

Adjacent sequences: A190498 A190499 A190500 * A190502 A190503 A190504

Keyword

nonn

Author

John W. Nicholson, May 11 2011

Extensions

Extended by T. D. Noe, May 11 2011

Modified the name as to match offset to A190502 and added leading term, John W. Nicholson, May 12 2011

Extended to n = 32 by John W. Nicholson, Dec 01 2012

Extended to n = 47, using A190502 data, by John W. Nicholson, Jan 31 2016

Status

approved