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

Author

Carmine Suriano, Sep 06 2010

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000040, A096701.

Programs

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 *)

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.