The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A015910 a(n) = 2^n mod n. 62
 0, 0, 2, 0, 2, 4, 2, 0, 8, 4, 2, 4, 2, 4, 8, 0, 2, 10, 2, 16, 8, 4, 2, 16, 7, 4, 26, 16, 2, 4, 2, 0, 8, 4, 18, 28, 2, 4, 8, 16, 2, 22, 2, 16, 17, 4, 2, 16, 30, 24, 8, 16, 2, 28, 43, 32, 8, 4, 2, 16, 2, 4, 8, 0, 32, 64, 2, 16, 8, 44, 2, 64, 2, 4, 68, 16, 18, 64, 2, 16, 80, 4, 2, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 2^n == 2 mod n if and only if n is a prime or a member of A001567 or of A006935. [Guy]. - N. J. A. Sloane, Mar 22 2012; corrected by Thomas Ordowski, Mar 26 2016 Known solutions to 2^n == 3 (mod n) are given in A050259. This sequence is conjectured to include every integer k >= 0 except k = 1. A036236 includes a proof that k = 1 is not in this sequence, and n = A036236(k) solves a(n) = k for all other 0 <= k <= 1000. - David W. Wilson, Oct 11 2011 It could be argued that a(0) := 1 would make sense, e.g., thinking of "mod n" as "in Z/nZ", and/or because (anything)^0 = 1. See also A112987. - M. F. Hasler, Nov 09 2018 REFERENCES Richard K. Guy, Unsolved Problems in Number Theory, F10. LINKS T. D. Noe, Table of n, a(n) for n=1..10000 Albert Frank, International Contest Of Logical Sequences, 2002 - 2003. Item 4 Albert Frank, Solutions of International Contest Of Logical Sequences, 2002 - 2003. Peter L. Montgomery, 65-digit solution. FORMULA a(2^k) = 0. - Alonso del Arte, Nov 10 2014 a(n) == 2^(n-phi(n)) mod n, where phi(n) = A000010(n). - Thomas Ordowski, Mar 26 2016 EXAMPLE a(7) = 2 because 2^7 = 128 = 2 mod 7. a(8) = 0 because 2^8 = 256 = 0 mod 8. a(9) = 8 because 2^9 = 512 = 8 mod 9. MAPLE A015910 := n-> modp(2 &^ n, n) ; # Zerinvary Lajos, Feb 15 2008 MATHEMATICA Table[PowerMod[2, n, n], {n, 85}] PROG (Maxima) makelist(power_mod(2, n, n), n, 1, 84); /* Bruno Berselli, May 20 2011 */ (PARI) a(n)=lift(Mod(2, n)^n) \\ Charles R Greathouse IV, Jul 15 2011 (Haskell) import Math.NumberTheory.Moduli (powerMod) a015910 n = powerMod 2 n n -- Reinhard Zumkeller, Oct 17 2015 (Magma) [Modexp(2, n, n): n in [1..100]]; // Vincenzo Librandi, Nov 09 2018 CROSSREFS Cf. A036236, A015911, A015921, A001567. Cf. A000079, A062173, A082495. Sequence in context: A144182 A037036 A055947 * A182256 A164993 A305572 Adjacent sequences: A015907 A015908 A015909 * A015911 A015912 A015913 KEYWORD nonn AUTHOR Robert G. Wilson v STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 15:01 EDT 2023. Contains 363019 sequences. (Running on oeis4.)