The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A318236 a(n) = (3*2^(4*n+3) + 1)/5. 1
 5, 77, 1229, 19661, 314573, 5033165, 80530637, 1288490189, 20615843021, 329853488333, 5277655813325, 84442493013197, 1351079888211149, 21617278211378381, 345876451382054093, 5534023222112865485, 88544371553805847757, 1416709944860893564109, 22667359117774297025741 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) is the smallest positive multiplicative inverse of 5 modulo 2^(4*n+3). In binary, a(n) is written as 10011001...1001101 where "1001" appears n times. When n approaches infinity we get the 2-adic expansion of 1/5: ...10011001101. Similarly, the 2-adic expansion of 1/3 is ...101010101011. LINKS Jianing Song, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (17,-16). FORMULA O.g.f.: (5 - 8*x)/((1 - x)*(1 - 16*x)). E.g.f.: (24*exp(16*x) + exp(x))/5. a(0) = 5, a(1) = 77; for n>1, a(n) = 17*a(n-1) - 16*a(n-2). EXAMPLE The smallest solution to 5*x == 1 (mod 8) is x = (3*2^3 + 1)/5 = 5. The smallest solution to 5*x == 1 (mod 128) is x = (3*2^7 + 1)/5 = 77. MATHEMATICA Table[(3 2^(4 n + 3) + 1) / 5, {n, 0, 20}] (* Vincenzo Librandi, Aug 24 2018 *) PROG (PARI) a(n) = (3*2^(4*n + 3) + 1)/5 (MAGMA) [(3*2^(4*n + 3) + 1)/5: n in [0..20]]; // Vincenzo Librandi, Aug 24 2018 CROSSREFS A007583 gives the smallest positive multiplicative inverse of 3 modulo 2^(2*n) and 2^(2*n+1), A299960 gives the smallest positive multiplicative inverse of 5 modulo 2^(4*n), 2^(4*n+1) and 2^(4*n+2). Sequence in context: A186662 A186660 A287041 * A009485 A188455 A015056 Adjacent sequences:  A318233 A318234 A318235 * A318237 A318238 A318239 KEYWORD nonn,easy AUTHOR Jianing Song, Aug 21 2018 STATUS approved

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

Last modified July 12 00:27 EDT 2020. Contains 335658 sequences. (Running on oeis4.)