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%I #10 Sep 04 2022 12:53:28
%S 4,9,33,65,77,161,371,38981,2561,568181
%N a(n) is the least semiprime p*q such that p*q-i*(p+q) is prime for i from 1 to n but not n+1.
%C 2*10^9 < a(10) <= 368470943651.
%e a(3) = 65 = 5*13 because 65-18 = 47, 65-2*18 = 29, and 65-3*18 = 11 are prime but 65-4*18 = -7 is not, and 65 is the least semiprime that works.
%p V:= Array(0..9): V[0]:= 4: count:= 1:
%p for n from 9 by 2 while count < 10 do
%p if numtheory:-bigomega(n) = 2 then
%p P:= numtheory:-factorset(n);
%p if nops(P) = 2 then s:= P[1]+P[2] else s:= 2*P[1] fi;
%p for i from 1 while isprime(n-i*s) do od:
%p v:=i-1;
%p if V[v] = 0 then V[v]:= n; count:= count+1; fi
%p fi
%p od:
%p convert(V, list);
%t primeQ[n_] := n > 0 && PrimeQ[n]; m[p_, q_] := Module[{i = 1}, While[primeQ[p*q - i*(p + q)], i++]; i]; seq[len_, nmax_] := Module[{s = Table[0, {len}], n = 1, c = 0, i, f}, While[c < len && n < nmax, f = FactorInteger[n]; If[f[[;; , 2]] == {2} || f[[;; , 2]] == {1, 1}, p = f[[1, 1]]; q = n/p; i = m[p, q]; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]]; n++]; s]; seq[10, 10^6] (* _Amiram Eldar_, Aug 29 2022 *)
%Y Cf. A001358, A356801.
%K nonn,more
%O 0,1
%A _J. M. Bergot_ and _Robert Israel_, Aug 29 2022
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