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%I #12 Mar 08 2022 11:37:54
%S 21,6,155,1111,77635,25877,16392913,78494323
%N a(n) is the first start of a sequence of exactly n members of A175648 under the map k -> 3*k+4.
%C a(n), 3*a(n)+4, 3*(3*a(n)+4)+4, ..., 3^(n-1)*a(n)+2*3^(n-1)-2 are in A175648 but 3^n*a(n)+2*3^n-2 is not.
%e a(3) = 155 because 155, 3*155+4 = 469 and 3*469+4 = 1411 are in A175648 but 3*1411+4 = 4237 is not (155 = 5*31, 159 = 3*53, 469 = 7*67, 473 - 11*43, 1411 = 17*83, and 1415 = 5*283 are semiprimes, but 4241 is prime).
%p f:= proc(n) option remember;
%p if numtheory:-bigomega(n)=2 and numtheory:-bigomega(n+4)=2 then 1 + procname(3*n+4) else 0 fi
%p end proc:
%p V:= Vector(7): count:= 0:
%p for nn from 1 while count < 7 do
%p v:= f(nn);
%p if v > 0 and V[v] = 0 then count:= count+1; V[v]:= nn; fi
%p od:
%p convert(V,list);
%Y Cf. A001358, A175648, A352132.
%K nonn,more
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Mar 05 2022
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