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

2, 5, 5, 17, 13, 137, 8021749, 1071065111, 1613902553, 1797595814863, 633925574060671, 22930603692243271, 5179852391836338871, 9648166508472058129

Offset: 1

Author

Christopher Hunt Gribble and T. D. Noe, Apr 02 2010

Keywords

• more
• nonn

Examples

			The first term is 2 since the 2 primes 2, 3 have a gap of 1, which is trivially symmetric about its center.
The second term is 5 since the 4 primes 5, 7, 11, 13 have gaps 2, 4, 2, which is symmetric about its center.
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.
		

Links

• N. Makarova and others, Distributed computing project, discussion at the scientific forum dxdy.ru (in Russian), Feb. 2015.
• Symmetric Prime Tuples, SPT test project
• Index entries for primes, gaps between

Crossrefs

Cf. A000040, A001223, A055380, A055381, A175309, A359440.

A variant of A055382.

Programs

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

Formula

a(n) = A175309(2n-1) (= A055382(n) for n>1). [M. F. Hasler, Apr 02 2010]

a(n) = A000040(k), where k = least number such that A359440(k+n-1) >= n-1. - Peter Munn, Jan 05 2023

Extensions

a(11) from Dmitry Petukhov, added by Max Alekseyev, Aug 08 2014

a(12) from an anonymous participant of the project, added by Natalia Makarova, Jul 16 2015

a(13)-a(14) from SPT test project, added by Dmitry Petukhov, Mar 16 2025