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

3, 5, 5, 17, 13, 137, 8021749, 1071065111, 1613902553, 1797595814863, 633925574060671, 22930603692243271, 5179852391836338871, 9648166508472058129

Offset: 1

Author

Jud McCranie, Jun 23 2000

Keywords

• more
• nonn

Comments

a(13) <= 5179852391836338871. The solution was found by the BOINC project "SPT test project". - Natalia Makarova, Dec 06 2023

Examples

			The first term is 3 since the 2 primes 3, 5 have a gap of 2, 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

• Discussion at the scientific forum dxdy.ru, Distributed computing project (in Russian)
• Symmetric Prime Tuples, SPT test project
• Index entries for primes, gaps between

Crossrefs

Cf. A001223, A055380, A055381, A175309.

See A081235 for another version.

Programs

Mathematica

Table[i = 1;
 While[x = Differences[Table[Prime[k + i], {k, 2 n}]];
x != Reverse[x], i++]; Prime[i + 1], {n, 6}] (* Robert Price, Oct 12 2019 *)

Formula

For n>1, a(n) = A081235(n) = A175309(2n-1).

Extensions

a(10) from Donovan Johnson, Mar 09 2008

Minor edits by N. J. A. Sloane, Apr 02 2010

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

a(12) from an anonymous participant of the project, added by Max Alekseyev, Jul 21 2015

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