A175309 a(n) = the smallest prime prime(k) such that prime(k+j) - prime(k+j-1) = prime(n+k+1-j) - prime(n+k-j) for all j with 1 <= j <= n.

2, 3, 5, 18713, 5, 683747, 17, 98303867, 13, 60335249851, 137, 1169769749111, 8021749, 3945769040698829, 1071065111, 159067808851610411, 1613902553

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)

a(19) = 1797595814863, a(21) = 633925574060671, a(23) = 22930603692243271. - Tomáš Brada, May 25 2020

Links

Table of n, a(n) for n = 1..17

BOINC project to search all up to 2^64

Formula

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

Mathematica

A175309[n_] := Module[{k},
   k = 1; While[! AllTrue[Range[n], Prime[k+#] - Prime[k+#-1] ==
        Prime[n+k+1-#] - Prime[n+k-#] &], k++]; Return[Prime[k]]];
Table[A175309[n], {n, 1, 7}]  (* Robert Price, Mar 27 2019 *)

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
(PARI) isok(p, n) = {my(k=primepi(p)); for (j=1, n, if (prime(k+j) - prime(k+j-1) != prime(n+k+1-j) - prime(n+k-j), return (0)); ); return (1); } \\ Michel Marcus, Apr 08 2017

Crossrefs

Cf. A006562, A051795, A081235, A081415, A096710, A055382.

Sequence in context: A072712 A046476 A263429 * A357323 A335304 A193888

Adjacent sequences: A175306 A175307 A175308 * A175310 A175311 A175312

Keyword

nonn,more

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

a(16) from BOINC project, added by Dmitry Petukhov, Apr 06 2017

Status

approved