A126605 Final three digits of 2^n.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 24, 48, 96, 192, 384, 768, 536, 72, 144, 288, 576, 152, 304, 608, 216, 432, 864, 728, 456, 912, 824, 648, 296, 592, 184, 368, 736, 472, 944, 888, 776, 552, 104, 208, 416, 832, 664, 328, 656, 312, 624, 248, 496, 992, 984, 968

Offset: 0

Author

Zak Seidov, Mar 13 2007

Keywords

• nonn
• base
• easy

Comments

Has period 100. Sequence of last four digits has period 500. Cf. A000855 Final two digits of 2^n, has period 20.

Links

• V. Raman and Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (first 103 terms from V. Raman)
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).

Crossrefs

Cf. A000689, A000855.

Programs

Magma

[Modexp(2, n, 1000): n in [0..110]]; // Vincenzo Librandi, Aug 16 2016

Mathematica

Table[PowerMod[2,n,1000],{n,0,1000}]

PARI

for(i=0,103,print(i" "(2^i)%1000)) \\ V. Raman, Sep 01 2012

Formula

For n > 54: a(n) = a(n-1) - a(n-50) + a(n-51). - Ray Chandler, Aug 09 2025