cp's OEIS Frontend

A081235 Smallest prime starting a sequence of 2n consecutive primes with symmetrical gaps about the center.

%I A081235 #44 Mar 24 2025 01:52:17
%S A081235 2,5,5,17,13,137,8021749,1071065111,1613902553,1797595814863,
%T A081235 633925574060671,22930603692243271,5179852391836338871,
%U A081235 9648166508472058129
%N A081235 Smallest prime starting a sequence of 2n consecutive primes with symmetrical gaps about the center.
%H A081235 N. Makarova and others, <a href="http://dxdy.ru/post1035725.html#p1035725">Distributed computing project</a>, discussion at the scientific forum dxdy.ru (in Russian), Feb. 2015.
%H A081235 Symmetric Prime Tuples, <a href="https://boinc.termit.me/adsl/">SPT test project</a>
%H A081235 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A081235 a(n) = A175309(2n-1) (= A055382(n) for n>1). [_M. F. Hasler_, Apr 02 2010]
%F A081235 a(n) = A000040(k), where k = least number such that A359440(k+n-1) >= n-1. - _Peter Munn_, Jan 05 2023
%e A081235 The first term is 2 since the 2 primes 2, 3 have a gap of 1, which is trivially symmetric about its center.
%e A081235 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 A081235 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.
%o A081235 (PARI) A081235(n) = { my(last=vector(n*=2,i,prime(i)), m, i=Mod(n-2,n)); forprime(p=last[n],default(primelimit), m=last[1+lift(i+2)]+last[1+lift(i++)]=p; for(j=1,n\2,last[1+lift(i-j)]+last[1+lift(i+j+1)]==m||next(2)); return(last[1+lift(i+1)]))} \\ _M. F. Hasler_, Apr 02 2010
%Y A081235 Cf. A000040, A001223, A055380, A055381, A175309, A359440.
%Y A081235 A variant of A055382.
%K A081235 more,nonn
%O A081235 1,1
%A A081235 _Christopher Hunt Gribble_ and _T. D. Noe_, Apr 02 2010
%E A081235 a(11) from _Dmitry Petukhov_, added by _Max Alekseyev_, Aug 08 2014
%E A081235 a(12) from an anonymous participant of the project, added by _Natalia Makarova_, Jul 16 2015
%E A081235 a(13)-a(14) from SPT test project, added by _Dmitry Petukhov_, Mar 16 2025