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a(n+1) = a(n) + 4^(n-1) a(n)^2.
(Formerly M3174)
2

%I M3174 #19 Dec 26 2021 20:38:39

%S 3,147,1383123,489735485064147,245597025618959718190041238775763,

%T 247062114274836300381127305147102564467751924522387062291401805739987

%N a(n+1) = a(n) + 4^(n-1) a(n)^2.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H James S. Hall, <a href="http://jlms.oxfordjournals.org/content/s1-28/3/285.extract">A remark on the primeness of Mersenne numbers</a>, J. London Math. Soc. 28, (1953), 285-287.

%H D. H. Lehmer. <a href="/A003009/a003009.pdf">Mathematical Reviews. Review of: Hall, James S. A remark on the primeness of Mersenne numbers. (1953)</a> [Annotated scanned copy]

%t RecurrenceTable[{a[3]==3,a[n]==a[n-1]+4^(n-2) a[n-1]^2},a,{n,3,10}] (* _Harvey P. Dale_, Jan 29 2014 *)

%K nonn,easy

%O 3,1

%A _N. J. A. Sloane_