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A018844
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Arises from generalized Lucas-Lehmer test for primality.
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3
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4, 10, 52, 724, 970, 10084, 95050, 140452, 1956244, 9313930, 27246964, 379501252, 912670090, 5285770564, 73621286644, 89432354890, 1025412242452, 8763458109130, 14282150107684, 198924689265124
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OFFSET
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1,1
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COMMENTS
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Apparently this was suggested by an article by R. M. Robinson.
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
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
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LINKS
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Jeppe Stig Nielsen, Table of n, a(n) for n = 1..1370
D. H. Lehmer, An Extended Theory of Lucas' Functions, Ann. Math. 31 (1930), 419-448. See p. 445.
Herb Savage et al., Re: Mersenne: starting values for LL-test
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FORMULA
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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}.
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
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
a(n) = sqrt(A206257(n) + 2). [Arkadiusz Wesolowski, Feb 08 2012]
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PROG
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(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
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CROSSREFS
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Sequence in context: A208236 A032495 A109387 * A007027 A192444 A197902
Adjacent sequences: A018841 A018842 A018843 * A018845 A018846 A018847
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KEYWORD
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easy,nonn
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AUTHOR
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Robert G. Wilson v
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STATUS
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approved
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