

A002091


From a Goldbach conjecture: the location of records in A185091.
(Formerly M2773 N1116)


9



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
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OFFSET

1,1


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


REFERENCES

Brian H. Mayoh, On the second Goldbach conjecture, Nordisk Tidskr. InformationsBehandling 6, 1966, 4850.
Emile Lemoine, L'intermédiaire 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).


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, 4850
Wikipedia, Lemoine's conjecture
Index entries for sequences related to Goldbach conjecture


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.


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


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

a(19)a(32) from Hugo Pfoertner, Sep 03 2011
a(33) from Jason Kimberley, a(34)a(40) from Hugo Pfoertner, Sep 09 2011
a(41)a(49) from Hugo Pfoertner, Sep 25 2011


STATUS

approved



