A050259 Numbers n such that 2^n == 3 (mod n).

1, 4700063497, 3468371109448915, 8365386194032363, 10991007971508067

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• more
• hard

Comments

No other terms below 10^18. - Max Alekseyev, Oct 17 2017

Terms were computed: a(2) by the Lehmers, a(3) by Max Alekseyev, a(4) and a(5) by Joe K. Crump, a(?) = 63130707451134435989380140059866138830623361447484274774099906755 by P.-L. Montgomery.

References

• R. Daniel Mauldin and S. M. Ulam, Mathematical problems and games. Adv. in Appl. Math. 8 (1987), pp. 281-344.

Links

• Joe K. Crump, 2^n mod n
• R. K. Guy, The Strong Law of Small Numbers, Amer. Math. Monthly 95 (1988), pp. 697-712. See example 13.
• R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
• Eric Weisstein's World of Mathematics, 2
• OEIS Wiki, 2^n mod n

Crossrefs

Cf. A001567, A036236, A015940, A015910.

Programs

Mathematica

m = 2; Join[Select[Range[m], Divisible[2^# - m, #] &],
Select[Range[m + 1, 10^6], PowerMod[2, #, #] == m &]] (* Robert Price, Oct 08 2018 *)

PARI

is(n)=Mod(2,n)^n==3 \\ Charles R Greathouse IV, Jun 11 2015