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!)
 A083205 a(1) = 1, then smallest number not included earlier such that a(n)*a(n+1) + 1 is an n-th power. 1
 1, 2, 4, 31, 26129, 466202136816810031, 10584868011442581563053546190350068005080430521324963528734180259722815036145 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence is infinite and a(n+1) <= ([a(n)+1]^n - 1)/a(n) when n is even, or a(n+1) <= ([a(n)-1]^n - 1)/a(n) when n is odd. To find a(6), we need an x such that x^5 = 1 (mod a(5)); then a(6) = (x^5 - 1)/a(5). The multiplicative group mod a(5) has order phi(a(5)) = 23296, which is not divisible by 5. So the only 5th root of 1 in this group is 1. x = 1 would give a(6) = 0, this is not allowed, so we take x to be the next representative of 1 mod a(5), i.e. a(5)+1. So a(6) = [(a(5)+1)^5 - 1]/a(5). - David Wasserman, Mar 02 2004 Next term is approximately 8.1*10^451. - David Wasserman, May 26 2004 LINKS EXAMPLE a(4) = 31, a(5) = 26129, 31*26129 + 1 = 810000 = 30^4. CROSSREFS Cf. A083203, A083204. Sequence in context: A051759 A051570 A082913 * A019542 A319223 A299783 Adjacent sequences:  A083202 A083203 A083204 * A083206 A083207 A083208 KEYWORD nonn AUTHOR Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 28 2003 EXTENSIONS More terms from David Wasserman, Mar 02 2004 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 March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)