A180457 Central term of nine successive primes whose average is a prime.

491, 617, 757, 1489, 1787, 2141, 2143, 2269, 3529, 3571, 4723, 5563, 6337, 6451, 6659, 6961, 6991, 7741, 7873, 7907, 8821, 10141, 10267, 10657, 12911, 13399, 14629, 15299, 16189, 16451, 16487, 17027, 18223, 18701, 19801, 19843, 19853, 19937

Offset

1,1

Comments

The average value is not always the central term (see A096701).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n)=[p(n-4)+p(n-3)+p(n-2)+p(n-1)+p(n)+p(n+1)+p(n+2)+p(n+3)+p(n+4)]/9.

Example

a(5)=1787 since (1753+1759+1777+1783+1787+1789+1801+1811+1823)/9=16083/9=1787 a prime.

Maple

Primes:= select(isprime, [seq(t, t=1..10^5, 2)]):
PSums:= ListTools[PartialSums](Primes):
Avgs:= [seq((PSums[i+9]-PSums[i])/9, i=1..nops(PSums)-9)]:
Pos:= select(t -> Avgs[t]::integer and isprime(Avgs[t]), [$1..nops(Avgs)]):
seq(Primes[Pos[i]+5], i=1..nops(Pos)); # Robert Israel, Apr 26 2016

Mathematica

Select[Partition[Prime[Range[2500]], 9, 1], PrimeQ[Mean[#]]&][[;; , 5]] (* Harvey P. Dale, Nov 20 2024 *)

Crossrefs

Cf. A000040, A096701.

Sequence in context: A051115 A273809 A060975 * A271664 A082079 A260925

Adjacent sequences: A180454 A180455 A180456 * A180458 A180459 A180460

Keyword

nonn

Author

Carmine Suriano, Sep 06 2010

Status

approved