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A090940
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a(n) = least odd prime distinct from earlier elements such that average of first n elements is prime.
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6
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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(3+7)/2 = 5, (3+7+5+13)/4 = 7.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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