A173572 Odd integers n such that 2^n == 4 (mod n).

1, 20737, 93527, 228727, 373457, 540857, 2231327, 11232137, 15088847, 15235703, 24601943, 43092527, 49891487, 66171767, 71429177, 137134727, 207426737, 209402327, 269165561, 302357057, 383696711, 513013327

Offset

1,2

Comments

The odd terms of A015921.

Also, nonprime integers n such that 2^(n-2) == 1 (mod n).

For all m, 2^A050259(m)-1 belongs to this sequence.

If n > 1 is a term and p is a primitive prime factor of 2^(n-2)-1, then n*p is also a term. Hence, the sequence is infinite. (Rotkiewicz 1984)

References

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

R. K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, Third Edition, 2004

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

Links

Max Alekseyev, Table of n, a(n) for n = 1..722 (all terms below 10^14)

C. K. Caldwell, Composite Numbers

A. Rotkiewicz, On the congruence 2^(n-2) == 1 (mod n). Math. Comp. 43 (1984), 271-272.

Maple

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

Mathematica

m = 4; Join[Select[Range[1, m, 2], Divisible[2^# - m, #] &], Select[Range[m + 1, 10^6, 2], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 12 2018 *)

Prog

(PARI) is(n) = n%2==1 && Mod(2, n)^n==Mod(4, n) \\ Jinyuan Wang, Feb 22 2019

Crossrefs

Cf. A015921, A050259, A173138, A002808.

Sequence in context: A180691 A103282 A013865 * A342391 A048960 A252331

Adjacent sequences: A173569 A173570 A173571 * A173573 A173574 A173575

Keyword

nonn

Author

Michel Lagneau, Feb 22 2010

Extensions

Edited and term 1 prepended by Max Alekseyev, Aug 09 2012

Status

approved