|
Search: id:A082552
|
|
|
| A082552 |
|
Number of sets of distinct primes, the greatest of which is prime(n), whose arithmetic mean is an integer. |
|
+0
1
|
|
| 1, 1, 2, 5, 6, 12, 21, 31, 58, 111, 184, 356, 665, 1223, 2260, 4227, 7930, 15095, 28334, 53822, 102317, 195012, 373001, 714405, 1370698, 2633383, 5067643, 9765457, 18846711, 36413982, 70431270, 136391723, 264384100, 512959093, 996173830
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
The sum of the first 23 primes gives 874 = 23*38, see A045345. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 02 2009]
|
|
EXAMPLE
|
a(4) = 5: prime(4) = 7 and the five sets are (5+7)/2 = 6, 7/1 = 7, (3+7)/2 = 5, (2+3+7)/3 = 4, (3+5+7)/3 = 5.
|
|
MAPLE
|
b:= proc(t, i, m, h) option remember; if h=0 then `if` (t=0, 1, 0) elif i<1 or h>i then 0 else b (t, i-1, m, h) +b((t+ithprime(i)) mod m, i-1, m, h-1) fi end: a := n-> add (b (ithprime(n) mod m, n-1, m, m-1), m=1..n): seq (a(n), n=1..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 02 2009]
|
|
MATHEMATICA
|
f[n_] := Block[{c = 0, k = n, lst = Prime@ Range@n, np = Prime@n, slst}, While[k < 2^n, slst = Subsets[lst, All, {k}]; If[Last@slst == np && Mod[Plus @@ slst, Length@slst] == 0, c++ ]; k++ ]; c]; Do[ Print[{n, f@n} // Timing], {n, 24}] (* Robert G. Wilson v *)
|
|
CROSSREFS
|
Cf. A051293, A072701.
Sequence in context: A058601 A108365 A064765 this_sequence A057683 A069480 A100613
Adjacent sequences: A082549 A082550 A082551 this_sequence A082553 A082554 A082555
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Naohiro Nomoto (n_nomoto(AT)yabumi.com), May 03 2003
|
|
EXTENSIONS
|
a(22)-a(24) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 19 2007
Corrected a(23) and extended by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 02 2009
|
|
|
Search completed in 0.002 seconds
|
