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%I #32 Aug 03 2020 18:12:34
%S 4,10,52,724,970,10084,95050,140452,1956244,9313930,27246964,
%T 379501252,912670090,5285770564,73621286644,89432354890,1025412242452,
%U 8763458109130,14282150107684,198924689265124
%N Arises from generalized Lucas-Lehmer test for primality.
%C Apparently this was suggested by an article by R. M. Robinson.
%C Starting values for Lucas-Lehmer test that result in a zero term (mod Mersenne prime Mp) after P-1 steps. - Jason Follas (jfollas_mersenne(AT)hotmail.com), Aug 01 2004
%C m belongs to the sequence iff m-2 is twice a square and m+2 is either three or six times a square. - _René Gy_, Jan 10 2019
%H Jeppe Stig Nielsen, <a href="/A018844/b018844.txt">Table of n, a(n) for n = 1..1370</a>
%H D. H. Lehmer, <a href="https://www.jstor.org/stable/1968235">An Extended Theory of Lucas' Functions</a>, Ann. Math. 31 (1930), 419-448. See p. 445.
%H Herb Savage et al., <a href="https://web.archive.org/web/20020304211255/http://www2.netdoor.com/~acurry/mersenne/archive1/0073.html">Re: Mersenne: starting values for LL-test</a>
%F Union of sequences a_1=4, a_2=52, a_{n}=14*a_{n-1} - a_{n-2} and b_1=10, b_2=970, b_{n}=98*b_{n-1} - b_{n-2}.
%F a[1]=14 (mod Mp), a[2]=52 (mod Mp), a[n]=(14*a[n-1]-a[n-2]) (mod Mp). - Jason Follas (jfollas_mersenne(AT)hotmail.com), Aug 01 2004
%F Though originally noted as the union of two sequences, when the first sequence (14*a[n-1]-a[n-2]) is evaluated modulo a Mersenne prime, the terms of the second sequence (98*b[n-1]-b[n-2]) will occur naturally (just not in numerical order). - Jason Follas (jfollas_mersenne(AT)hotmail.com), Aug 01 2004
%F a(n) = sqrt(A206257(n) + 2). [_Arkadiusz Wesolowski_, Feb 08 2012]
%o (PARI) listUpTo(n)=a=List([4,52]);while(1,m=14*a[#a]-a[#a-1];m>n&&break();listput(a,m));b=List([10,970]);while(1,m=98*b[#b]-b[#b-1];m>n&&break();listput(b,m));setunion(Set(a),Set(b)) \\ _Jeppe Stig Nielsen_, Aug 03 2020
%K easy,nonn
%O 1,1
%A _Robert G. Wilson v_
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