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A219953
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a(1) = 1; for n > 1, a(n) = smallest integer > a(n-1) such that a(n)*a(i)+1 is semiprime for all 1 <= i <= n-1.
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1
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1, 3, 8, 38, 86, 318, 504, 3600, 8132, 83160, 116850, 202272, 399126, 6190086, 8756916, 25253676, 309709400, 1112878446, 1478724036, 11062089360, 97331025386
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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a(1) = 1 by definition.
a(2) = 3: 3 > 1, and 1*3 + 1 = 4 = 2^2 is semiprime.
a(3) = 8: 8 > 3, and 1*8 + 1 = 9 = 3^2 is semiprime, and 3*8 + 1 = 25 = 5^2 is semiprime.
a(4) = 38: 38 > 8, and 1*38 + 1 = 39 = 3*13 is semiprime, and 3*38 + 1 = 115 = 5*23 is semiprime, and 8*38 + 1 = 305 = 5*61 is semiprime.
The resulting semiprimes are:
4;
9, 25;
39, 115, 305;
87, 259, 689, 3269;
319, 955, 2545, 12085, 27349;
...
(End)
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MAPLE
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option remember;
if n= 1 then
1;
else
for a from procname(n-1)+1 do
issp := true ;
for i from 1 to n-1 do
if numtheory[bigomega]( a*procname(n-i)+1) = 2 then
;
else
issp := false;
break ;
end if;
end do:
if issp then
return a;
end if;
end do:
end if;
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MATHEMATICA
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a = {1}; Do[k = a[[n - 1]] + 1; While[! AllTrue[(k a[[n - #]] + 1) & /@ Range@ (n - 1), Total[Last /@ FactorInteger@ #] == 2 &], k++]; AppendTo[a, k], {n, 2, 13}]; a (* Michael De Vlieger, Jul 26 2015, Version 10 *)
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PROG
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(PARI) ok(v, n, k) = {v[n] = k; for (j=1, n-1, if (bigomega(1+v[n]*v[j]) != 2, return (0)); ); return (1); }
lista(nn) = {print1(k=1, ", "); v = [k]; for (n=2, nn, k = v[n-1]+1; v = concat(v, k); while (! ok(v, n, k), k++); v[n] = k; print1(k, ", "); ); } \\ Michel Marcus, Jul 26 2015
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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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EXTENSIONS
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STATUS
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approved
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