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A121561 The number of iterations of "subtract the largest prime less than or equal to the current value" to go from n to the limiting value 0 or 1.

%I A121561 #14 Jul 27 2022 02:15:58
%S A121561 0,1,1,1,1,1,1,1,2,2,1,1,1,1,2,2,1,1,1,1,2,2,1,1,2,2,2,2,1,1,1,1,2,2,
%T A121561 2,2,1,1,2,2,1,1,1,1,2,2,1,1,2,2,2,2,1,1,2,2,2,2,1,1,1,1,2,2,2,2,1,1,
%U A121561 2,2,1,1,1,1,2,2,2,2,1,1,2,2,1,1,2,2,2,2,1,1,2,2,2,2,2,2,1,1,2,2,1,1,1,1,2
%N A121561 The number of iterations of "subtract the largest prime less than or equal to the current value" to go from n to the limiting value 0 or 1.
%C A121561 Number of steps to go from n to A121559(n).
%C A121561 The sequence has the form of blocks of numbers; see A121562 for the lengths of those blocks.
%H A121561 Robert G. Wilson v, <a href="/A121561/b121561.txt">Table of n, a(n) for n = 1..100000</a>
%e A121561 a(9) = 2 because there are 2 steps in going from 9 to 0 in A121559: 9 mod 7 = 2 and 2 mod 2 = 0.
%t A121561 LrgstPrm[n_] := Block[{k = n}, While[ !PrimeQ@ k, k-- ]; k]; f[n_] := Block[{c = 0, d = n}, While[d > 1, d = d - LrgstPrm@d; c++ ]; c]; Array[f, 105] (* _Robert G. Wilson v_, Feb 29 2008 *)
%o A121561 (Python)
%o A121561 from sympy import prevprime
%o A121561 def a(n): return 0 if n == 0 or n == 1 else 1 + a(n - prevprime(n+1))
%o A121561 print([a(n) for n in range(1, 106)]) # _Michael S. Branicky_, Jul 26 2022
%Y A121561 Cf. A121559, A064722, a(n)=1: A093515, a(n)=2: A093513, a(n)=3: A138026, a(n)=4: A138027.
%K A121561 easy,nonn
%O A121561 1,9
%A A121561 _Kerry Mitchell_, Aug 07 2006