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

1,1

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.

Links

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

Example

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.

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}]]

Prog

(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))}

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).

Sequence in context: A234831 A280983 A184651 * A208490 A272021 A345718

Adjacent sequences: A123083 A123084 A123085 * A123087 A123088 A123089

Keyword

nonn

Author

Zak Seidov, Sep 27 2006

Status

approved