OFFSET
1,12
COMMENTS
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2
FORMULA
a(n) = eta(T(n))- eta(T(n-1)).
EXAMPLE
Write the numbers 1, 2, ... in a triangle with n terms in the n-th row; a(n) = number of Ramanujan primes in n-th row.
Triangle begins
1 (0 Ramanujan primes, eta(1) = 0)
2 3 (1 Ramanujan primes, eta(3) - eta(1) = 1)
4 5 6 (0 Ramanujan primes, eta(6) - eta(3) = 0)
7 8 9 10 (0 Ramanujan primes, eta(10) - eta(6) = 0)
11 12 13 14 15 (1 Ramanujan primes, eta(15) - eta(10) = 1)
16 17 18 19 20 21 (1 Ramanujan primes, eta(21) - eta(15) = 1)
MATHEMATICA
PROG
(Perl) use ntheory ":all"; sub a191225 { my $n = shift; ramanujan_prime_count( (($n-1)*$n)/2+1, ($n*($n+1))/2 ); } say a191225($_) for 1..10; # Dana Jacobsen, Dec 30 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Nicholson, May 27 2011
STATUS
approved