A103622 Smallest arithmetic mean of n distinct primes.

2, 4, 4, 7, 6, 11, 10, 13, 12, 17, 16, 21, 20, 24, 24, 29, 26, 32, 32, 36, 36, 41, 38, 45, 44, 49, 48, 53, 52, 58, 58, 63, 62, 68, 66, 72, 70, 77, 76, 83, 80, 87, 86, 92, 90, 97, 96, 102, 100, 108, 106, 113, 110, 118, 116, 123, 122, 129, 126, 133, 132, 139, 138, 145, 142

Offset: 1

Author

Giovanni Teofilatto, Mar 25 2005

Keywords

• easy
• nonn

Comments

Often a(2n+1) = a(2n) - 1. - Robert G. Wilson v, Jan 19 2007

Examples

			a(1)=2 because (2)/1=2,
a(2)=4 because (3+5)/2=4,
a(3)=4 because (2+3+7)/3=4,
a(4)=7 because (3+5+7+13)/4=7,
a(5)=6 because (2+3+5+7+13)/5=6,
a(6)=11 because (3+5+7+11+17+23)/6=11,
a(7)=10 because (2+3+5+7+11+13+29)/7=10,
a(8)=13 because (3+5+7+11+13+17+19+29)/8=13,
a(9)=12 because (2+3+5+7+11+13+17+19+31)/9=12,
a(10)=17 because (3+5+7+11+13+17+19+23+29+43)/10=17, etc.
		

Crossrefs

Cf. A072701.

Programs

Mathematica

f[n_] := Block[{k = 1, lst = Prime@ Range[ If[ OddQ@ n, 1, 2], n + 3]}, While[ Mod[Plus @@ Flatten@Subsets[lst, {n}, {k}], n] != 0, k++ ]; (Plus @@ Flatten@ Subsets[lst, {n}, {k}])/n]; Array[f, 65] (* Robert G. Wilson v, Jan 19 2007 *)

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jan 19 2007