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%I #17 Sep 03 2021 01:53:26
%S 1,1,2,3,4,7,8,15,16,17,18,35,36,71,72,73,74,147,148,295,296,297,298,
%T 595,596,597,598,599,600,1199,1200,2399,2400,2401,2402,2403,2404,4807,
%U 4808,4809,4810,9619,9620,19239,19240,19241,19242,38483,38484,38485
%N a(1) = a(2) = 1; for n>2, a(n+1) = a(n) + a(n-1) iff n is prime, otherwise a(n+1) = a(n) + 1.
%H Ivan Neretin, <a href="/A113050/b113050.txt">Table of n, a(n) for n = 1..1000</a>
%e a(3) = 2 because 3-1 = 2 is prime, hence a(3) = a(2) + a(1) = 1 + 1 = 2.
%e a(4) = 3 because 4-1 = 3 is prime, hence a(4) = a(3) + a(2) = 2 + 1 = 3.
%e a(5) = 4 because 5-1 = 4 is not prime, hence a(5) = a(4) + 1 = 3 + 1 = 4.
%e a(6) = 7 because 6-1 = 5 is prime, hence a(6) = a(5) + a(4) = 4 + 3 = 7.
%e a(7) = 8 because 7-1 = 6 is not prime, hence a(7) = a(6) + 1 = 7 + 1 = 8.
%e a(8) = 15 because 8-1 = 7 is prime, hence a(8) = a(7) + a(6) = 8 + 7 = 15.
%t a[1] = a[2] = 1; a[n_] := a[n] = If[ PrimeQ[n - 1], a[n - 1] + a[n - 2], a[n - 1] + 1]; Table[ a[n], {n, 50}] (* _Robert G. Wilson v_, Oct 14 2005 *)
%Y Cf. A000040, A000045, A113051.
%K easy,nonn
%O 1,3
%A _Jonathan Vos Post_, Oct 12 2005
%E Corrected and extended by _Robert G. Wilson v_, Oct 14 2005
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