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

1, 4700063497, 3468371109448915, 8365386194032363, 10991007971508067

Offset

1,2

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

Table of n, a(n) for n=1..5.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001567, A036236, A015940, A015910.

Sequence in context: A199631 A124977 A128172 * A249972 A233494 A175568

Adjacent sequences: A050256 A050257 A050258 * A050260 A050261 A050262

Keyword

nonn,more,hard

Author

Eric W. Weisstein

Status

approved