A094932 Primes that represent some mean of 4 consecutive (2 smaller, itself, 1 larger) primes.

113, 199, 317, 619, 863, 1069, 1129, 1789, 2861, 3089, 3169, 3259, 3677, 3739, 4733, 4973, 5419, 5591, 6581, 7649, 7963, 8243, 8297, 8629, 9973, 10463, 10799, 10909, 11093, 11119, 12347, 12379, 12619, 12983, 14011, 14327, 15331, 15649, 16007

Offset

4,1

Comments

A prime number prime(n) is in the sequence if the arithmetic mean of the 4 nearby primes, measured by A034963(n-2)/4, equals one plus the prime. - R. J. Mathar, Nov 15 2019

Links

Table of n, a(n) for n=4..42.

Formula

a(n) = If[(Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/4-Prime[n-1]-1==0, then Prime[n-1]

Example

113 is in the list because the arithmetic mean of 107, 109, 113, and 127 is A034963(28)/4 = 456/4 = 114, and 114 = 1+113.

Mathematica

a=Table[If[(Prime[n-3]+Prime[n-2]+Prime[n-1]+Prime[n])/4-Prime[n-1]-1==0, Prime[n-1], 0], {n, 4, 2004}] a0=Delete[Union[Sort[a]], 1]

Crossrefs

Sequence in context: A124585 A173594 A074982 * A173595 A142276 A054695

Adjacent sequences: A094929 A094930 A094931 * A094933 A094934 A094935

Keyword

nonn,less

Author

Roger L. Bagula, Jun 17 2004

Extensions

Definition rephrased. - R. J. Mathar, Nov 15 2019

Status

approved