1,1

The next term if it exists is > 32452843 = 2000000-th prime. Can someone prove this sequence is finite and full? - Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 26 2001

To prove that 127 is the last prime, we need to show that prime gaps satisfy prime(k)-prime(k-1)<sqrt(prime(k-1)) for k>31. Although it is easy to verify this inequality for all known prime gaps, there is no proof for all gaps. - T. D. Noe (noe(AT)sspectra.com), Jul 25 2006

Eric Weisstein's World of Mathematics, MathWorld: Prime Gaps

Prime(k) is in the sequence if prime(k)^2 (mod prime(k-1)) is odd.

The first prime with a prime lower than itself is 3. This squared is 9, which when divided by the previous prime 2 leaves remainder 1, which is odd. So 3 is in the sequence. 11 is not in the sequence because 11^2, when divided by the previous prime 7, leaves a remainder of 121 (mod 7) = 2, which is even.

Prime /@ Select[ Range[ 2, 100 ], OddQ[ Mod[ Prime[ # ]^2, Prime[ # - 1 ] ] ] & ]

Cf. A038702.

Cf. A058188 (number of primes between prime(n) and prime(n)+sqrt(prime(n))).

Sequence in context: A058580 A161682 A079373 this_sequence A163586 A074931 A023226

Adjacent sequences: A038700 A038701 A038702 this_sequence A038704 A038705 A038706

nonn

N. Fernandez (primeness(AT)borve.org), May 01 2000

More terms from Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 26 2001