A173138 Composite numbers k such that 2^(k-4) == 1 (mod k).

4, 40369, 673663, 990409, 1697609, 2073127, 6462649, 7527199, 7559479, 14421169, 21484129, 37825753, 57233047, 130647919, 141735559, 179203369, 188967289, 218206489, 259195009, 264538057, 277628449, 330662479, 398321239, 501126487, 506958313, 612368311, 767983759

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

Michael S. Branicky, Table of n, a(n) for n = 1..62

Example

4 is a term: 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
(Python)
from sympy import isprime, prime, nextprime
def afind(k=4):
    while True:
        if pow(2, k-4, k) == 1 and not isprime(k): print(k, end=", ")
        k += 1
afind() # Michael S. Branicky, Mar 21 2022

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

Typo in a(13) corrected by Georg Fischer, Mar 19 2022

a(24) and beyond from Michael S. Branicky, Mar 21 2022

Status

approved