This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A255595 Sylvester's sequence modulo 109. 1
 2, 3, 7, 43, 63, 92, 89, 94, 23, 71, 66, 40, 35, 101, 73, 25, 56, 29, 50, 53, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32, 12, 24, 8, 57, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For most small primes, it's easy to see that they have no multiples in Sylvester's sequence (A000058) by considering the sequence modulo the prime in question. For example, Sylvester's sequence modulo 41 is 2, 3, 7, 2, 3, 7, 2, 3, 7, ... But with 109, it isn't until A000058(25) modulo 109 that we encounter the repeated value of 32. From this point forward, the period {32, 12, 24, 8, 57} is infinitely repeated. The table in Sylvester (1880) is missing the 57. REFERENCES J. J. Sylvester, Postscript to Note on a Point in Vulgar Fractions. American Journal of Mathematics Vol. 3, No. 4 (Dec., 1880): 389, Table. LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1). FORMULA a(0) = 2, a(n) = a(n - 1)^2 - a(n - 1) + 1 mod 109. EXAMPLE a(4) = 43 because a(3) = 7 and 7^2 - 7 + 1 = 43. a(5) = 63 because 43^2 - 43 + 1 = 1807 = 63 mod 109. MATHEMATICA sylv109[0] := 2; sylv109[n_] := sylv109[n] = Mod[sylv109[n - 1](sylv109[n - 1] - 1) + 1, 109]; Table[sylv109[n], {n, 0, 108}] CROSSREFS Sequence in context: A030087 A106864 A282027 * A085682 A267505 A267506 Adjacent sequences:  A255592 A255593 A255594 * A255596 A255597 A255598 KEYWORD nonn,easy AUTHOR Alonso del Arte, Mar 25 2015 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 December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)