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 A158923 a(1) = 2, a(n) = a(n-1) + round(log(a(n-1))) for n >= 2. 5

%I

%S 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 78,82,86,90,94,99,104,109,114,119,124,129,134,139,144,149,154,159,

%U 164,169,174,179,184,189,194,199,204,209,214,219,224,229,234,239,244,249

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

%C Each interval (a(n-1), a(n)] asymptotically contains one prime power on the average.

%H Daniel Forgues, <a href="/A158923/b158923.txt">Table of n, a(n) for n = 1..100000</a>

%t NestList[# + Round@ Log[#] &, 2, 60] (* _Michael De Vlieger_, Nov 05 2020 *)

%o (Python)

%o from math import log

%o print(2)

%o a_last = n = 2

%o while n >= 2:

%o a = a_last + int(log(a_last) + 0.5)

%o print(a)

%o a_last = a

%o n += 1 # _Ya-Ping Lu_, Oct 24 2020

%Y 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 Cf. A158925, "Accumulated excess or deficit of prime powers in (1, A158924(n)]" (Partial sums of A158924).

%Y Cf. A000961, "Prime powers p^k (p prime, k >= 0)."

%Y Cf. A025528, "Number of prime powers <= n with exponents >0."

%K nonn

%O 1,1

%A _Daniel Forgues_, Mar 30 2009

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Last modified July 29 13:28 EDT 2021. Contains 346346 sequences. (Running on oeis4.)