A294390 a(n) = 2^(n-4) mod n, for n >= 4.

1, 2, 4, 1, 0, 5, 4, 7, 4, 5, 2, 8, 0, 15, 4, 12, 16, 11, 14, 3, 16, 2, 10, 5, 8, 11, 4, 4, 0, 17, 30, 23, 4, 14, 24, 20, 16, 36, 4, 27, 12, 32, 6, 6, 16, 8, 14, 26, 40, 20, 22, 13, 16, 29, 22, 37, 16, 23, 8, 32, 0, 2, 4, 42, 52, 35, 64, 9, 40, 64, 28, 23, 20, 30, 4

Offset: 4

Author

Enrique Navarrete, Oct 29 2017

Keywords

• nonn
• easy
• look

Comments

Every nonnegative integer seems to appear in the sequence, and every integer seems to appear in the sequence of first differences (see link).

From Robert Israel, Dec 04 2017: (Start)

a(n) = 0 iff n>=8 is a power of 2.

a(n) = 1 iff n=4 or n is in A033984.

a(n) = 2 iff n>=4 is in A015925 and is not divisible by 4. (End)

Examples

			For n=9, 2^5 = 32 == 5 mod 9.
		

Links

• Robert Israel, Table of n, a(n) for n = 4..10000
• Enrique Navarrete, Sequences derived from residues of 2^n (mod n)

Crossrefs

Cf. A015910, A015925, A033984, A294389.

Programs

Magma

[Modexp(2, n-4, n): n in [4..120]]; // G. C. Greubel, Dec 27 2024

Maple

A294390:=n->2&^(n-4) mod n: seq(A294390(n), n=4..150); # Wesley Ivan Hurt, Nov 30 2017

Mathematica

Array[Mod[2^(# - 4), #] &, 75, 4] (* Michael De Vlieger, Dec 02 2017 *)
Array[PowerMod[2,#-4,#]&,80,4] (* Harvey P. Dale, Dec 01 2018 *)

PARI

a(n) = lift(Mod(2, n)^(n-4)); \\ Michel Marcus, Oct 30 2017

SageMath

print([power_mod(2, n-4, n) for n in range(4, 101)]) # G. C. Greubel, Dec 27 2024

Extensions

More terms from Michel Marcus, Oct 30 2017