A102655 Numbers that are the arithmetic mean of four successive primes.

9, 12, 15, 18, 22, 30, 38, 42, 46, 55, 60, 68, 81, 87, 102, 105, 108, 114, 120, 127, 139, 144, 149, 155, 165, 175, 181, 186, 195, 200, 215, 228, 232, 241, 247, 253, 260, 265, 270, 278, 291, 306, 312, 318, 333, 341, 352, 357, 363, 381, 387, 399, 420, 426, 431

Offset: 1

Author

Giovanni Teofilatto, Feb 02 2005

Keywords

• easy
• nonn

Examples

			a(1) = 9 because (5+7+11+13)/4=9;
a(2) = 12 because (7+11+13+17)/4=12;
a(3) = 15 because (11+13+17+19)/4=15.
		

Crossrefs

Cf. A034963.

Programs

Mathematica

Select[ Table[ Sum[ Prime[i], {i, n, n + 3}]/4, {n, 83}], IntegerQ[ # ] &] (* Robert G. Wilson v, Feb 04 2005 *)
Select[MovingAverage[Prime[Range[500]],4],IntegerQ] (* Harvey P. Dale, Aug 10 2012 *)

Formula

4*n = A000040(i) + A000040(i+1) + A000040(i+2) + A000040(i+3) for some i>=1.

Extensions

Edited by Robert G. Wilson v and W. Neville Holmes, Feb 04 2005