

A108897


Numbers k such that 60*k^2 + 30*k  30 + 1 is a twin prime pair.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 21, 22, 37, 39, 40, 41, 42, 51, 53, 54, 59, 64, 71, 80, 82, 83, 94, 102, 103, 105, 106, 110, 114, 118, 128, 143, 144, 156, 166, 167, 169, 172, 183, 192, 193, 199, 218, 222, 224, 227, 234, 235, 236, 253, 258, 259, 265, 266
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OFFSET

1,2


COMMENTS

Some consecutive terms in this sequence are (102:103), (105:106), (143:144), ... (1320071:1320072), (1320250:1320251) ... Conjecture: There are infinitely many of these consecutive pairs.


REFERENCES

David Wells, Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons, 2005, p. 231.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

1 is in the sequence since 60*1^2 + 30*1  30 = 60 and {59, 61} are twin primes.


MATHEMATICA

lst={}; Do[If[PrimeQ[60*n^2+30*n301]&&PrimeQ[60*n^2+30*n30+1], AppendTo[lst, n]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 08 2008 *)


CROSSREFS

Cf. A001097, A001359, A006512.
Sequence in context: A151767 A213517 A173899 * A023767 A023794 A032948
Adjacent sequences: A108894 A108895 A108896 * A108898 A108899 A108900


KEYWORD

easy,nonn


AUTHOR

Jason Earls, Jul 16 2005


STATUS

approved



