

A083205


a(1) = 1, then smallest number not included earlier such that a(n)*a(n+1) + 1 is an nth power.


1




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

Table of n, a(n) for n=1..7.


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



