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A123078 Integers that are the arithmetic mean of 1000 consecutive primes. 2
10820, 15682, 19672, 23340, 25067, 33873, 37387, 39377, 47782, 59635, 75249, 82619, 86378, 87303, 89198, 92217, 97495, 111989, 131987, 133441, 162286, 164644, 178666, 181532, 182196, 200088, 203450, 215280, 215612, 218527, 221526, 229733 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Corresponding indices of the first primes are: 812, 1323, 1731, 2097, 2268, 3121, 3456, 3645, 4428, 5518, 6914, 7569, 7899, 7980, 8146, 8412, 8875 A102655 Numbers which are the arithmetic mean of four successive primes. A122040 Numbers which are equal to arithmetic mean of six successive primes. A122480 Least k>2 such that n is equal to arithmetic mean of k consecutive primes. A122808 Least number that is the arithmetic mean of n (but no fewer) consecutive primes.
LINKS
FORMULA
Conjecture: a(n) ~ 1000 n log n. - Charles R Greathouse IV, Oct 23 2012
EXAMPLE
(p(812)+p(813)+...+p(812+998)+p(812+999))/1000=10820, p(n)=n-th prime.
MATHEMATICA
Select[Table[Sum[Prime[k], {k, n, n + 999}]/1000, {n, 50000}], IntegerQ] - Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006
Select[Mean/@Partition[Prime[Range[25000]], 1000, 1], IntegerQ] (* Harvey P. Dale, Jul 27 2022 *)
CROSSREFS
Sequence in context: A190115 A203394 A144716 * A235254 A237190 A065321
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 27 2006
EXTENSIONS
More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)