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A190275
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Semiprimes of the form p*(p^2 - p + 1).
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6
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6, 21, 301, 2041, 296341, 486877, 2666437, 3420301, 4304341, 7152001, 38159521, 42387097, 54296677, 95235601, 158048281, 229971241, 265434901, 383712781, 454166017, 775307917, 972261181, 1063290841, 1304557801, 1392422041, 1730882401, 1863895261, 2631883561, 2879450461, 3714274297, 3845297341, 4070454361, 4256780041, 4849695001, 5328809461, 5722533337, 5838483601, 7218898681, 7841065621
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OFFSET
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1,1
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COMMENTS
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This sequence is infinite, assuming Schinzel's Hypothesis H.
Related to Rassias Conjecture ("for any odd prime p there are primes q < r such that p*q = q + r + 1") setting p = q. Generalization can be achieved by removing semiprimality condition and accepting p^e, e >= 2.
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LINKS
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EXAMPLE
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a(1) = 6 = 2*3 = 2*(2^2-2+1).
a(2) = 21 = 3*7 = 3*(3^2-3+1).
a(3) = 301 = 7*43 = 7*(7^2-7+1).
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MAPLE
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seq(`if`(isprime((ithprime(i)^2-ithprime(i)+1))=true, (ithprime(i)^2-ithprime(i)+1)*ithprime(i), NULL), i=1..300);
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MATHEMATICA
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p = Select[Prime@ Range@ 500, PrimeQ[#^2 - # + 1] &]; p (p^2 - p + 1) (* Giovanni Resta, Jul 22 2019 *)
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PROG
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CROSSREFS
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Cf. A065508 (primes p such that p^2-p+1 is prime).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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