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

Offset

1,1

Links

Table of n, a(n) for n=1..12.

N. Makarova and others, Distributed computing project, discussion at the scientific forum dxdy.ru (in Russian), Feb. 2015.

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

Example

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.

Prog

(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

Crossrefs

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

A variant of A055382.

Sequence in context: A014442 A281793 A259036 * A219586 A082534 A165659

Adjacent sequences: A081232 A081233 A081234 * A081236 A081237 A081238

Keyword

more,nonn

Author

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

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

Status

approved