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A298943
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Lower of two consecutive Mersenne prime exponents with record first difference.
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0
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2, 3, 7, 19, 31, 127, 607, 1279, 2281, 3217, 4423, 11213, 23209, 44497, 132049, 216091, 1398269, 3021377, 6972593, 13466917
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OFFSET
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1,1
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COMMENTS
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Conjecture: The sequence is infinite.
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LINKS
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EXAMPLE
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A000043(7) = 19 and A134458(7) = 12, which is larger than A134458(i) for any i < 7, so 19 is a term of the sequence.
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MATHEMATICA
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Block[{s = Partition[MersennePrimeExponent@ Range@ 45, 2, 1], t}, t = Map[Differences, s][[All, 1]]; Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]]][[All, 1]] (* Michael De Vlieger, Jan 31 2018 *)
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PROG
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(PARI) LL(e) = my(n, h); n = 2^e-1; h = Mod(2, n); for (k=1, e-2, h=2*h*h-1); return(0==h) \\ after Joerg Arndt in A000043
my(r=0, p=2); forprime(q=3, , if(LL(q), if(q-p > r, print1(p, ", "); r=q-p); p=q))
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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