A233866 Ramanujan primes A104272 that are primes p(k) such that (k+1)*p(k)>k*p(k+1).

2, 11, 17, 29, 41, 59, 71, 101, 107, 127, 149, 179, 227, 229, 281, 307, 311, 347, 349, 419, 431, 439, 461, 487, 569, 599, 641, 643, 659, 739, 769, 809, 821, 823, 853, 857, 937, 967, 983, 1009, 1019, 1031, 1049, 1061, 1087, 1091, 1151, 1187, 1217, 1229

Offset

1,1

Comments

Non-Ramanujan primes (A174635) that are primes p(k) such that (k+1)*p(k)>k*p(k+1): 137, 163, 191, 197, 223, 277, 379, 397, 457, 499, 521, 613, 617, 673, 757, 859, 877, 907, 1093, 1181, 1213, 1223, 1231,...

Primes p(k) such that (k+1)*p(k)> k*p(k+1): 2, 11, 17, 29, 41, 59, 71,...

primes p(k) such that (k+1)*p(k) - k*p(k+1)=1: 2, 11,...

Primes p(m) such that (m+1)*p(m) < m*p(m+1): 3, 5, 7, 13, 19, 23, 31,...

Links

Table of n, a(n) for n=1..50.

Example

Ramanujan prime 2 is in this sequence because 2 = p(1) such that (1 + 1)*p(1) = 2*2 = 4 > 1*p(1 + 1) = 3;
Ramanujan prime 11 is in this sequence because 11 = p(5) such that (5 + 1)*p(5) = 6*11 = 66 > 5*p(5 + 1) = 65.

Crossrefs

Sequence in context: A194658 A104272 A214934 * A117155 A186782 A141176

Adjacent sequences: A233863 A233864 A233865 * A233867 A233868 A233869

Keyword

nonn,less

Author

Irina Gerasimova, Dec 17 2013

Status

approved