

A123086


Numbers which are the arithmetic mean of 1000000 consecutive primes.


3



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



