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A081235
Smallest prime starting a sequence of 2n consecutive primes with symmetrical gaps about the center.
12
2, 5, 5, 17, 13, 137, 8021749, 1071065111, 1613902553, 1797595814863, 633925574060671, 22930603692243271
OFFSET
1,1
LINKS
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
A variant of A055382.
Sequence in context: A014442 A281793 A259036 * A219586 A082534 A165659
KEYWORD
more,nonn
AUTHOR
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