A212541 Let p_n=prime(n), n>=1. Then a(n) is the maximal prime p which differs from p_n, for which the intervals (p/2,p_n/2), (p,p_n], if p<p_n, or the intervals (p_n/2,p/2), (p_n,p], if p>p_n, contain the same number of primes, and a(n)=0, if no such prime p exists.

0, 11, 11, 11, 7, 17, 13, 29, 29, 23, 41, 41, 37, 47, 43, 59, 53, 67, 61, 0, 97, 97, 97, 97, 89, 0, 107, 103, 127, 149, 109, 149, 149, 151, 137, 139, 167, 167, 163, 179, 173, 0, 227, 229, 229, 233, 229, 227, 223, 211, 199, 0, 0, 263, 263, 257, 0, 281, 281

Offset

1,2

Comments

a(n)<p_n if and only if p_n is Ramanujan prime (A104272).

a(n)=0 if and only if p_n is a peculiar prime, i.e., simultaneously Ramanujan and Labos (A080359) prime (see sequence A164554).

Links

Table of n, a(n) for n=1..59.

V. Shevelev, Ramanujan and Labos primes, their generalizations, and classifications of primes, J. Integer Seq. 15 (2012) Article 12.5.4

Formula

If p_n is not a Ramanujan prime, then a(n) = A104272(n-pi(p_n/2)).

Example

Let n=4, p_n=7. Since 7 is not Ramanujan prime, then a(4) = A104272(4-pi(3.5)) = A104272(2) = 11.

Crossrefs

Cf. A212493, A104272, A080359, A164554.

Sequence in context: A152986 A252838 A366717 * A087994 A100755 A171902

Adjacent sequences: A212538 A212539 A212540 * A212542 A212543 A212544

Keyword

nonn

Author

Vladimir Shevelev and Peter J. C. Moses, May 20 2012

Status

approved