cp's OEIS Frontend

A055382 Smallest prime starting a sequence of 2n consecutive odd primes with symmetrical gaps about the center.

%I A055382 #51 Mar 24 2025 01:51:47
%S A055382 3,5,5,17,13,137,8021749,1071065111,1613902553,1797595814863,
%T A055382 633925574060671,22930603692243271,5179852391836338871,
%U A055382 9648166508472058129
%N A055382 Smallest prime starting a sequence of 2n consecutive odd primes with symmetrical gaps about the center.
%C A055382 a(13) <= 5179852391836338871. The solution was found by the BOINC project "SPT test project". - _Natalia Makarova_, Dec 06 2023
%H A055382 Discussion at the scientific forum dxdy.ru, <a href="http://dxdy.ru/post1035725.html#p1035725">Distributed computing project</a> (in Russian)
%H A055382 Symmetric Prime Tuples, <a href="https://boinc.termit.me/adsl/">SPT test project</a>
%H A055382 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A055382 For n>1, a(n) = A081235(n) = A175309(2n-1).
%e A055382 The first term is 3 since the 2 primes 3, 5 have a gap of 2, which is trivially symmetric about its center.
%e A055382 The second term is 5 since the 4 primes 5, 7, 11, 13 have gaps 2, 4, 2, which is symmetric about its center.
%e A055382 The twelve primes 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193 have gaps 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2 - symmetric about the middle, so a(6) = 137.
%t A055382 Table[i = 1;
%t A055382  While[x = Differences[Table[Prime[k + i], {k, 2 n}]];
%t A055382 x != Reverse[x], i++]; Prime[i + 1], {n, 6}] (* _Robert Price_, Oct 12 2019 *)
%Y A055382 Cf. A001223, A055380, A055381, A175309.
%Y A055382 See A081235 for another version.
%K A055382 more,nonn
%O A055382 1,1
%A A055382 _Jud McCranie_, Jun 23 2000
%E A055382 a(10) from _Donovan Johnson_, Mar 09 2008
%E A055382 Minor edits by _N. J. A. Sloane_, Apr 02 2010
%E A055382 a(11) from _Dmitry Petukhov_, added by _Max Alekseyev_, Aug 08 2014
%E A055382 a(12) from an anonymous participant of the project, added by _Max Alekseyev_, Jul 21 2015
%E A055382 a(13)-a(14) from SPT test project, added by _Dmitry Petukhov_, Mar 16 2025