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A138026 Numbers k where A121561(k) = 3.

%I A138026 #8 Jun 08 2025 19:26:24
%S A138026 122,123,148,190,208,209,220,221,250,292,302,303,326,327,346,418,430,
%T A138026 476,477,518,519,532,533,538,539,556,586,628,629,640,670,671,700,718,
%U A138026 782,783,796,806,807,820,838,848,849,872,873,896,897,902,903,928,962
%N A138026 Numbers k where A121561(k) = 3.
%H A138026 Robert Israel, <a href="/A138026/b138026.txt">Table of n, a(n) for n = 1..10000</a>
%p A138026 filter:= proc(n)
%p A138026   local t;
%p A138026   t:= n-prevprime(n+1);
%p A138026   if t <= 1 then return false fi;
%p A138026   t:= t-prevprime(t+1);
%p A138026   if t <= 1 then return false fi;
%p A138026   isprime(t) or isprime(t-1)
%p A138026 end proc:
%p A138026 select(filter,[$2..1000]); # _Robert Israel_, Jan 15 2019
%t A138026 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]; lst = {}; Do[ If[f@n == 3, AppendTo[lst,n]], {n, 10^3}]; lst
%Y A138026 Cf. A121561, A093515, A093513, A138027.
%K A138026 nonn
%O A138026 1,1
%A A138026 _Robert G. Wilson v_, Feb 27 2008