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A173138 Composite numbers n such that 2^(n-4) == 1 (mod n). 3
4, 40369, 673663, 990409, 1697609, 2073127, 6462649, 7527199, 7559479, 14421169, 21484129, 37825753, 5723304, 130647919, 141735559, 179203369, 188967289, 218206489, 259195009, 264538057, 277628449, 330662479, 398321239 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Besides the initial term, the sequence coincides with A033984 and consists of the odd terms >7 of A015924.

REFERENCES

A. E. Bojarincev, Asymptotic expressions for the n-th composite number, Univ. Mat. Zap. 6:21-43 (1967). - In Russian.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.

LINKS

Table of n, a(n) for n=1..23.

EXAMPLE

For n = 4, 2^(4 - 4) = 1 (mod 4).

MAPLE

with(numtheory): for n from 1 to 100000000 do: a:= 2^(n-4)- 1; b:= a / n; c:= floor(b): if b = c and tau(n) <> 2 then print (n); else fi; od:

MATHEMATICA

Select[Range[500000000], !PrimeQ[#]&&PowerMod[2, #-4, #]==1&] (* Harvey P. Dale, Nov 23 2011 *)

PROG

(PARI) is(n)=!isprime(n) && n>1 && Mod(2, n)^(n-4)==1 \\ Charles R Greathouse IV, Nov 23 2011

CROSSREFS

Cf. A002808, A005381, A033984

Sequence in context: A001376 A053937 A259160 * A275587 A132638 A046882

Adjacent sequences:  A173135 A173136 A173137 * A173139 A173140 A173141

KEYWORD

nonn

AUTHOR

Michel Lagneau, Feb 10 2010

EXTENSIONS

Simplified the definition, added cross-reference to A033984 R. J. Mathar, May 18 2010

More terms from Harvey P. Dale, Nov 23 2011

STATUS

approved

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Last modified August 20 17:05 EDT 2017. Contains 290836 sequences.