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A175309 a(n) = the smallest prime p(k) such that p(k+j) - p(k+j-1) = p(n+k+1-j) - p(n+k-j) for all j with 1 <= j <= n. 10
2, 3, 5, 18713, 5, 683747, 17, 98303867, 13, 60335249851, 137, 1169769749111, 8021749, 3945769040698829, 1071065111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From M. F. Hasler, Apr 02 2010: (Start)

Also: Start of the first sequence of n+1 consecutive primes symmetrically distributed w.r.t. their barycenter, e.g., [2,3], [3,5,7], [5,7,11,13], [18713, 18719, 18731, 18743, 18749]. With this definition, it would make sense to prefix the sequence with an initial term a(0)=2.

Sequence A081235 (or A055382, which is essentially the same) consists of every other term of this sequence. (End)

LINKS

Table of n, a(n) for n=1..15.

FORMULA

a(2n-1) = A081235(n) (= A055382(n) for n>1). [M. F. Hasler, Apr 02 2010]

PROG

(PARI) a(n)={ my( last=vector(n++, 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. A006562, A051795, A081415, A096710, A055382.

Sequence in context: A072712 A046476 A263429 * A193888 A141186 A078682

Adjacent sequences:  A175306 A175307 A175308 * A175310 A175311 A175312

KEYWORD

more,nonn

AUTHOR

Leroy Quet, Mar 27 2010

EXTENSIONS

Terms through a(12) were calculated by (in alphabetical order) Franklin T. Adams-Watters, Hans Havermann and D. S. McNeil

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

a(14) from Dmitry Petukhov, added by Max Alekseyev, Nov 03 2014

STATUS

approved

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Last modified March 27 08:26 EDT 2017. Contains 284146 sequences.