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 A025003 a(1) = 2; a(n+1) = a(n)-th nonprime, where nonprimes begin at 1. 4
 2, 4, 8, 14, 22, 33, 48, 66, 90, 120, 156, 202, 256, 322, 400, 494, 604, 734, 888, 1067, 1272, 1512, 1790, 2107, 2472, 2890, 3364, 3903, 4515, 5207, 5990, 6875, 7868, 8984, 10238, 11637, 13207, 14959, 16909, 19075, 21483, 24173, 27149, 30436, 34080, 38103 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Index of first occurrence of n in A090532. Let b(n) (n >= 0) be the smallest integer k >= 1 that takes n steps to reach 1 iterating the map f: k -> k - pi(k). The sequence {b(n), n >= 0} begins 1, 2, 4, 8, 14, 22, 33, 48, 66, 90, 120, 156, ... and agrees with the present sequence except for b(0). - Ya-Ping Lu, Sep 07 2020 LINKS FORMULA a(n) = min(k: f^n(k) = 1), where f = A062298 and n-fold iteration of f is denoted by f^n. - Ya-Ping Lu, Sep 07 2020 EXAMPLE From Ya-Ping Lu, Sep 07 2020: (Start) a(1) = 2 because f(2) = 2 - pi(2) = 1 and m(2) = 1; For the integer 3, since f(3) = 1. m(3) = 1, which is not bigger than m(1) or m(2). So, 3 is not a term in the sequence; a(2) = 4 because f^2(4) = f(2) = 1 and m(4) = 2; a(3) = 8 because f^3(8) = f^2(4) = 1 and m(8) = 3. (End) MAPLE N:= 50: # to get a(0)..a(N) V:= Array(0..N): V:= 1: V:= 2: m:= 2: p:= 3: g:= 1: n:= 1: do   if g+p-m-1 >= V[n] then     m:= V[n]+m-g;     n:= n+1;     V[n]:= m;     if n = N then break fi;     g:= V[n-1];   else     g:= g+p-m;     m:= p+1;     p:= nextprime(m);   fi; od; convert(V, list); # Robert Israel, Sep 08 2020 PROG (Python) from sympy import prime, primepi n_last = 0 pi_last = 0 ct_max = -1 for n in range(1, 100001):     ct = 0     pi = pi_last + primepi(n) - primepi(n_last)     n_c = n     pi_c = pi     while n_c > 1:         nc -= pi_c         ct += 1         pi_c -= primepi(n_c + pi_c) - primepi(n_c)     if ct > ct_max:         print(n)         ct_max = ct     n_last = n     pi_last = pi # Ya-Ping Lu, Sep 07 2020 CROSSREFS Cf. A000040, A000720, A014688, A014689, A062298, A090532, A332086, A337334. Sequence in context: A025196 A084626 A090533 * A087151 A053798 A305497 Adjacent sequences:  A025000 A025001 A025002 * A025004 A025005 A025006 KEYWORD nonn AUTHOR STATUS approved

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Last modified August 10 16:03 EDT 2022. Contains 356039 sequences. (Running on oeis4.)