A123086 Numbers which are the arithmetic mean of 1000000 consecutive primes.

11860710, 19524458, 30466003, 57980974, 63924288, 90876871, 98124660, 100711080, 107813124, 130902871, 130920140, 133345096, 137765645, 149928192, 187600902, 214934436, 223349020, 235566127, 238768532, 239934902, 264189816, 270196572, 278851320, 285021997

Offset: 1

Author

Zak Seidov, Sep 27 2006

Keywords

• nonn

Comments

Corresponding indices of the first primes are: 275775, 740092, 1383476, 2948575, 3280201, 4764532, 5159226, 5299723, 5684491, 6926061, 6926985, 7056669, 7292768, 7940227, 9929283, 11358606, 11796712, 12431386, 12597486, 12657959, 13911879, 14221421, 14666768, 14983910, 15100050.

Examples

			11860710 is in the sequence since (p(275775) + p(275776) + ... + p(275775+999998) + p(275775+999999)) / 1000000 = 11860710 where p(n) is the n-th prime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..467

Crossrefs

Cf. A102655 (arithmetic mean of four successive primes).

Cf. A122040 (arithmetic mean of six successive primes).

Cf. A122480 (arithmetic mean of k consecutive primes).

Cf. A122808 (arithmetic mean of n, but no fewer, consecutive primes).

Programs

Mathematica

Timing[s = 7472966967499 ; a = 2; b = 15485863; Do[s = s - a + (b = NextPrime[b]); a = NextPrime[a]; If[Mod[s, 10^6] < 1, Print[s/10^6]], {10^8}]]

PARI

{s = 7472966967499 ; a = 2; b = 15485863; for (k = 1, 10^9,
if(s%10^6 < 1, print( s/10^6)); b = nextprime (b + 2);
s = s - a + b; a = nextprime (a + 1))}