Search: id:A038703
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%I A038703
%S A038703 3,5,17,29,37,127
%N A038703 Primes p such that p^2 mod q is odd, where q is the previous prime.
%C A038703 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
%C A038703 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
%H A038703 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeGaps.html">MathWorld: Prime Gaps</a>
%F A038703 Prime(k) is in the sequence if prime(k)^2 (mod prime(k-1)) is odd.
%e A038703 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.
%t A038703 Prime /@ Select[ Range[ 2, 100 ], OddQ[ Mod[ Prime[ # ]^2, Prime[ # - 
               1 ] ] ] & ]
%Y A038703 Cf. A038702.
%Y A038703 Cf. A058188 (number of primes between prime(n) and prime(n)+sqrt(prime(n))).
%Y A038703 Sequence in context: A058580 A161682 A079373 this_sequence A163586 A074931 
               A023226
%Y A038703 Adjacent sequences: A038700 A038701 A038702 this_sequence A038704 A038705 
               A038706
%K A038703 nonn
%O A038703 1,1
%A A038703 N. Fernandez (primeness(AT)borve.org), May 01 2000
%E A038703 More terms from Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 26 
               2001

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