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a(n) = b(n)-th highest positive integer not equal to any a(k), 1 <= k <= n-1, where b(n) = noncomposite numbers = A008578(n).
1

%I #4 Mar 13 2015 22:51:17

%S 1,3,5,8,11,16,19,24,27,32,39,42,49,54,57,62,69,76,79,86,91,94,101,

%T 106,113,122,127,130,135,138,143,158,163,170,173,184,187,194,201,206,

%U 213,220,223,234,237,242,245,258,271,276,279,284,291,294,305,312,319,326

%N a(n) = b(n)-th highest positive integer not equal to any a(k), 1 <= k <= n-1, where b(n) = noncomposite numbers = A008578(n).

%C a(1) = 1, a(n) = A014688(n-1) = (n-1)-th prime + n - 1 for n >= 2. a(n) = A090178(n) - 1 = n-th noncomposite number + n - 1 for n >= 2.

%F a(1) = 1, a(n) = a(n-1) + A008578(n+1) - A008578(n) + 1 for n >= 2. a(1) = 1, a(2) = 3, a(n) = a(n-1) + A001223(n) + 1 for n >= 3. a(1) = 1, a(n) = n - 1 + A000040(n-1) = n - 1 + A008578(n) = n - 1 + A158611(n+1) for n >= 2.

%e A008578(4) = 5, so a(4) = 8 = 5th highest positive integer not equal to 1, 3, or 5 (the values of a(k), 1 <= k <= 3).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Oct 28 2009