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A090940
a(n) = least odd prime distinct from earlier elements such that average of first n elements is prime.
6
3, 7, 5, 13, 37, 73, 23, 71, 29, 109, 103, 19, 41, 293, 59, 251, 683, 107, 31, 223, 67, 151, 523, 127, 227, 131, 347, 83, 137, 197, 139, 907, 163, 503, 173, 389, 179, 863, 743, 211, 2671, 271, 701, 281, 101, 277, 4507, 367, 661, 373, 883, 383, 2927, 431, 541, 433
OFFSET
1,1
COMMENTS
a(n) is the smallest not yet used odd prime such that (a(1)+...+a(n))/n is prime.
Conjectured to include all odd prime numbers. - David W. Wilson, Nov 23 2012
LINKS
Zak Seidov and Alois P. Heinz, Table of n, a(n) for n = 1..10000
EXAMPLE
(3+7)/2 = 5, (3+7+5+13)/4 = 7.
MAPLE
q:= proc(n) option remember; is(n<3) end:
a:= proc(n) option remember; local k, p;
if n=1 then 3 else for k while q(k) or
irem(s(n-1)+ithprime(k), n, 'p')>0 or not isprime(p)
do od; q(k):= true; ithprime(k) fi
end:
s:= proc(n) option remember; a(n) +`if`(n<2, 0, s(n-1)) end:
seq (a(n), n=1..100); # Alois P. Heinz, Nov 21 2012
MATHEMATICA
a = 3; s = {a}; sm = a; Do[Do[p = Prime[k]; If[FreeQ[s, p] && PrimeQ[(sm + p)/i], sm = sm + p; AppendTo[s, p]; Break[]], {k, 3, 1000000}], {i, 2, 1000}]; s (* Zak Seidov, Nov 21 2012 *)
CROSSREFS
Cf. A090941.
Sequence in context: A065283 A352670 A268261 * A090916 A342701 A184162
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Dec 29 2003
EXTENSIONS
Corrected and extended by Ray Chandler, Dec 31 2003
Definition corrected by David W. Wilson, Nov 23 2012
STATUS
approved