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A356825
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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.
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1
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OFFSET
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0,1
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COMMENTS
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2*10^9 < a(10) <= 368470943651.
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LINKS
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EXAMPLE
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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.
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MAPLE
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V:= Array(0..9): V[0]:= 4: count:= 1:
for n from 9 by 2 while count < 10 do
if numtheory:-bigomega(n) = 2 then
P:= numtheory:-factorset(n);
if nops(P) = 2 then s:= P[1]+P[2] else s:= 2*P[1] fi;
for i from 1 while isprime(n-i*s) do od:
v:=i-1;
if V[v] = 0 then V[v]:= n; count:= count+1; fi
fi
od:
convert(V, list);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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