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A166945
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Records of first differences of A166944.
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15
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2, 3, 7, 13, 43, 139, 313, 661, 1321, 2659, 5419, 10891, 22039, 44383, 88801, 177841, 355723, 713833, 1427749, 2860771, 5725453, 11461141, 22933441, 45895573, 91793059, 183616423, 367232911, 734482123, 1468965061, 2937930211, 5875882249, 11751795061, 23503590559, 47007181621, 94014363763
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OFFSET
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1,1
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COMMENTS
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Conjecture. Each term of the sequence is the greater of a pair of twin primes (A006512).
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LINKS
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Table of n, a(n) for n=1..35.
E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol.11(2008), Article 08.2.8. arXiv:0710.3217 [math.NT]
V. Shevelev, An infinite set of generators of primes based on the Rowland idea and conjectures concerning twin primes, arXiv:0910.4676 [math.NT], 2009.
V. Shevelev, Three theorems on twin primes, arXiv:0911.5478 [math.NT], 2009-2010.
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MATHEMATICA
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Reap[Print[old = r = 2]; Sow[old]; For[n = 2, n <= 10^6, n++, d = GCD[old, If[OddQ[n], n-2, n]]; If[d>r, r=d; Print[d]; Sow[d]]; old += d]][[2, 1]] (* Jean-François Alcover, Nov 03 2018, from PARI *)
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PROG
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(PARI) print1(old=r=2); for(n=2, 1e11, d=gcd(old, if(n%2, n-2, n)); if(d>r, r=d; print1(", "d)); old+=d) \\ Charles R Greathouse IV, Oct 13 2017
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CROSSREFS
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Cf. A166944, A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293.
Sequence in context: A007996 A206579 A349327 * A257393 A273814 A085872
Adjacent sequences: A166942 A166943 A166944 * A166946 A166947 A166948
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev, Oct 24 2009, Nov 05 2009
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EXTENSIONS
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6 more terms from R. J. Mathar, Nov 19 2009; extension beginning with a(19) from Benoit Cloitre (private communication to Vladimir Shevelev)
a(25), a(26) from D. S. McNeil, Dec 13 2010
a(27)-a(30) from Charles R Greathouse IV, Oct 13 2017
a(31)-a(35) from Charles R Greathouse IV, Oct 17 2017
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STATUS
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approved
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