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A002091
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From a Goldbach conjecture: the location of records in A185091.
(Formerly M2773 N1116)
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8
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3, 9, 19, 21, 55, 115, 193, 323, 611, 1081, 1571, 10771, 13067, 16321, 44881, 57887, 93167, 189947, 404939, 442307, 1746551, 3383593, 3544391, 5056787, 7480667, 25619213, 87170987, 404940757, 526805663, 707095391, 1009465507, 1048720723, 5315914139
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A stronger version of the second Goldbach conjecture (every odd number can be expressed as the sum of 3 primes) states that every odd number n > 5 can be written as n = 2*p + q, p, q prime. The conjecture was posed by E. Lemoine and later by H. Levy. The article by B.H. Mayoh assumes q {1,prime}. For the representations of n minimizing q, the sequence gives the value of n at which a larger q than for all representations of j<n is required. The new record value of q is given in A002092. The corresponding sequences for q prime and q=1 excluded are A194828 and A194829. - Hugo Pfoertner, Sep 03 2011
n is in this list when (n+1)/2 is the index of a record in A185091.
Checked up to n=10^13. a(50) is > 10^13. - Hugo Pfoertner, Sep 25 2011
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REFERENCES
| Brian H. Mayoh, On the second Goldbach conjecture, Nordisk Tidskr. Informations-Behandling 6, 1966, 48-50.
Emile Lemoine, L'intermédiare des mathématiciens, 1 (1894), 179; ibid 3 (1896), 151.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Hugo Pfoertner, Table of n, a(n) for n = 1..49
Brian H. Mayoh, On the second Goldbach conjecture, BIT Numerical Mathematics 6 (1966) 1, 48-50
Wikipedia, Lemoine's conjecture
Index entries for sequences related to Goldbach conjecture
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EXAMPLE
| a(3)=19, because it is the first number for which q=5 is required. 3=2*1+1, 5=2*2+1, 7=2*3+1, 9=2*3+3, 11=2*5+1, 13=2*5+3, 15=2*7+1, 17=2*7+3, 19=2*7+5.
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CROSSREFS
| Cf. A002092 [values of q], A194828, A194829 [equivalent with q=1 excluded].
Cf. A185091.
Sequence in context: A097267 A043097 A084670 * A056259 A056682 A032670
Adjacent sequences: A002088 A002089 A002090 * A002092 A002093 A002094
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| a(19)-a(32) from Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 03 2011
a(33) from Jason Kimberley, a(34)-a(40) from Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 09 2011
a(41)-a(49) from Hugo Pfoertner (hugo(AT)pfoertner.org), Sep 25 2011
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