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A158923 a(1) = 2, a(n) = a(n-1) + round(log(a(n-1))) for n >= 2.

%I A158923 #16 Nov 05 2020 15:40:30
%S A158923 2,3,4,5,7,9,11,13,16,19,22,25,28,31,34,38,42,46,50,54,58,62,66,70,74,
%T A158923 78,82,86,90,94,99,104,109,114,119,124,129,134,139,144,149,154,159,
%U A158923 164,169,174,179,184,189,194,199,204,209,214,219,224,229,234,239,244,249
%N A158923 a(1) = 2, a(n) = a(n-1) + round(log(a(n-1))) for n >= 2.
%C A158923 Each interval (a(n-1), a(n)] asymptotically contains one prime power on the average.
%H A158923 Daniel Forgues, <a href="/A158923/b158923.txt">Table of n, a(n) for n = 1..100000</a>
%t A158923 NestList[# + Round@ Log[#] &, 2, 60] (* _Michael De Vlieger_, Nov 05 2020 *)
%o A158923 (Python)
%o A158923 from math import log
%o A158923 print(2)
%o A158923 a_last = n = 2
%o A158923 while n >= 2:
%o A158923     a = a_last + int(log(a_last) + 0.5)
%o A158923     print(a)
%o A158923     a_last = a
%o A158923     n += 1 # _Ya-Ping Lu_, Oct 24 2020
%Y A158923 Cf. A158924, "Number of prime powers - 1 in interval (A158923(n-1), A158923(n)] expressing the excess or deficit relative to the asymptotic average of 1."
%Y A158923 Cf. A158925, "Accumulated excess or deficit of prime powers in (1, A158924(n)]" (Partial sums of A158924).
%Y A158923 Cf. A000961, "Prime powers p^k (p prime, k >= 0)."
%Y A158923 Cf. A025528, "Number of prime powers <= n with exponents >0."
%K A158923 nonn
%O A158923 1,1
%A A158923 _Daniel Forgues_, Mar 30 2009