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A072820
Largest number of distinct primes to represent n as arithmetic mean.
2
1, 1, 3, 3, 5, 4, 5, 5, 7, 6, 9, 8, 9, 9, 11, 10, 11, 11, 13, 12, 13, 13, 15, 14, 17, 15, 17, 16, 17, 17, 19, 18, 19, 19, 21, 20, 23, 21, 23, 22, 23, 23, 25, 24, 25, 25, 27, 26, 27, 27, 29, 28, 29, 28, 29, 29, 31, 30, 31, 31, 33, 32, 33, 33, 35, 33, 35, 34, 37, 35, 37, 36, 37, 37
OFFSET
2,3
EXAMPLE
a(20) = 13: (2+3+5+7+11+13+17+19+23+29+31+41+59)/13 = 20. [corrected by Jean-François Alcover, Nov 10 2020]
MAPLE
sp:= proc(i) option remember; `if`(i=1, 2, sp(i-1) +ithprime(i)) end:
b:= proc(n, i, t) local h; if n<0 then 0 elif n=0 then `if`(t=0, 1, 0) elif i=2 then `if`(n=2 and t=1, 1, 0) else h := b(n, prevprime(i), t); b(n, i, t):= `if`(h>0, h, b(n-i, prevprime(i), t-1)) fi end:
a:= proc(n) local i, k; if n<4 then 1 else for k from 2 while sp(k)/k<=n do od: do k:= k-1; if b(k*n, nextprime(k*n -sp(k-1)-1), k)>0 then break fi od; k fi end: seq(a(n), n=2..50); # Alois P. Heinz, Aug 03 2009
MATHEMATICA
sp[i_] := sp[i] = If[i == 1, 2, sp[i - 1] + Prime[i]];
b[n_, i_, t_] := b[n, i, t] = Module[{h}, Which[n < 0, 0, n == 0, If[t == 0, 1, 0], i == 2, If[n == 2 && t == 1, 1, 0], True, h = b[n, NextPrime[i, -1], t]; If[h > 0, h, b[n - i, NextPrime[i, -1], t - 1]]]];
a[n_] := a[n] = Module[{k}, If[n < 4, 1, For[k = 2, sp[k]/k <= n, k++]; While[True, k = k - 1; If[b[k n, NextPrime[k n - sp[k - 1] - 1], k] > 0, Break[]]]; k]];
Table[Print[n, " ", a[n]]; a[n], {n, 2, 100}] (* Jean-François Alcover, Nov 13 2020, after Alois P. Heinz *)
CROSSREFS
Cf. A072701.
Sequence in context: A290284 A258802 A358241 * A204004 A131950 A116192
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 15 2002
EXTENSIONS
More terms from Alois P. Heinz, Aug 03 2009
STATUS
approved