A090940 a(n) = least odd prime distinct from earlier elements such that average of first n elements is prime.

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

Adjacent sequences: A090937 A090938 A090939 * A090941 A090942 A090943

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