A122040 -id:A122040 - cp's OEIS frontend

A122531 Primes equal to arithmetic mean of 6 successive primes; or primes in A122040(n).

101, 139, 227, 419, 431, 883, 1021, 1231, 1303, 1433, 1447, 1543, 1583, 1621, 1721, 1993, 2243, 2251, 2351, 2531, 2539, 2591, 2693, 2707, 2713, 2753, 3359, 3461, 3541, 3911, 4091, 4153, 4423, 4447, 5011, 5233, 5527, 5869, 6029, 6091, 6469, 6481, 6569

Offset: 1

Alexander Adamchuk, Sep 17 2006

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A122040.

Select[Table[Sum[Prime[k],{k,n,n+5}],{n,1,1000}]/6,IntegerQ[ #1]&&PrimeQ[ #1]&]
Select[Mean/@Partition[Prime[Range[900]],6,1],PrimeQ] (* Harvey P. Dale, Apr 18 2018 *)

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

Original entry on oeis.org

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

Zak Seidov, Sep 27 2006

nonn

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.

			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.

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

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).

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}]]

{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))}

A123078 Integers that are the arithmetic mean of 1000 consecutive primes.

Original entry on oeis.org

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

Offset: 1

Zak Seidov, Sep 27 2006

nonn

Corresponding indices of the first primes are: 812, 1323, 1731, 2097, 2268, 3121, 3456, 3645, 4428, 5518, 6914, 7569, 7899, 7980, 8146, 8412, 8875, ... .

			(p(812)+p(813)+...+p(812+998)+p(812+999))/1000=10820, p(n)=n-th prime.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A102655, A122040, A122480, A122808.

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 *)

Conjecture: a(n) ~ 1000 n log n. - Charles R Greathouse IV, Oct 23 2012

More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Oct 10 2006

cp's OEIS Frontend

A122531 Primes equal to arithmetic mean of 6 successive primes; or primes in A122040(n).

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

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A123078 Integers that are the arithmetic mean of 1000 consecutive primes.

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