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a(n) = ((n+1)^n-(n-1)^n)/2+1.
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Table[((n+1)^n-(n-1)^n)/2+1, {n, 20}] (* Harvey P. Dale, Oct 27 2019 *)
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_Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), _, Jun 14 2011
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Cf. A000040.
The next prime in the sequence , after 2, 5 and 29, has at least 888 digits (n >= 349).
The next prime in the sequence has at least 888 digits (n >= 349).
2, 5, 29, 273, 3377, 51013, 1048577, 908609, 18640961, 432891137, 10000000001, 11225320101, 321504185345, 100498283728818, 10079828372881, 343360783937537, 12627774819845669, 498676704524517377, 21046391759976988929, 945381827279671853057, 45032132922921758270917