A072821 Largest prime that can appear in any representation of n as an arithmetic mean of distinct primes.

1, 1, 7, 7, 13, 13, 23, 19, 29, 29, 43, 37, 53, 47, 71, 61, 79, 73, 103, 89, 113, 109, 139, 127, 157, 139, 179, 163, 199, 181, 223, 199, 241, 227, 271, 241, 293, 271, 317, 293, 349, 317, 379, 349, 409, 379, 439, 409, 463, 439, 503, 463, 523, 499, 571, 523, 601

Offset

2,3

Comments

Thanks to John W. Layman for inspiration.

Links

Alois P. Heinz, Table of n, a(n) for n = 2..100

Reinhard Zumkeller, Representing integers as arithmetic means of primes

Example

a(6) = 13, as 13 is the largest prime in 6 = (5+7)/2 = (2+3+13)/3 = (2+5+11)/3 = (2+3+5+7+13)/5.

Maple

sp:= proc(i) option remember; `if` (i=1, 2, sp(i-1) +ithprime(i)) end:
b:= proc(n, i, t) option remember; 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, 2, 0) else `if` (b(n-i, prevprime(i), t-1)>0, i, b(n, prevprime(i), t)) fi end:
a:= proc(n) local s, k; s:= 1; for k from 2 while sp(k)/k<=n do s:= max (s, b(k*n, nextprime (k*n -sp(k-1)-1), k)) od: s end:
seq(a(n), n=2..40); # 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] = Which[n < 0, 0, n == 0, If[t == 0, 1, 0], i == 2,  If[n == 2 && t == 1, 1, 0], True, If[b[n - i, NextPrime[i, -1], t - 1] > 0, i, b[n, NextPrime[i, -1], t]]];
a[n_] := Module[{s, k}, s = 1; For[k = 2, sp[k]/k <= n, k++, s = Max[s, b[k*n, NextPrime[k*n - sp[k - 1] - 1], k]]]; s];
Table[a[n], {n, 2, 60}] (* Jean-François Alcover, Feb 13 2018, after Alois P. Heinz *)

Crossrefs

Cf. A072701.

Sequence in context: A143429 A168301 A335895 * A038589 A332304 A317790

Adjacent sequences: A072818 A072819 A072820 * A072822 A072823 A072824

Keyword

nonn

Author

Reinhard Zumkeller, Jul 15 2002

Extensions

More terms from Alois P. Heinz, Aug 03 2009

Status

approved