OFFSET
1,3
COMMENTS
The absolute value is relevant only when a(n) = 0 in which case a(n+1) = gcd(a(n),n) = n.
It is conjectured that a(n) = 0 implies that n is prime, see A186253. (This is the sequence {u(n)} mentioned there.)
a(A186253(n)-1) = 1; a(A186253(n)) = 0; a(A186253(n)+1) = A186253(n). - Reinhard Zumkeller, Sep 07 2015
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
EXAMPLE
a(2) = a(1) - gcd(a(1),1) = 1 - 1 = 0.
a(3) = |a(2) - gcd(a(2),2)| = gcd(0,2) = 2 is prime.
a(3+2) = a(5) = 0, a(6) = gcd(0,5) = 5 is prime.
a(6+5) = a(11) = 0, a(12) = gcd(0,11) = 11 is prime.
a(12+11) = a(23) = 0, a(24) = 23 is prime.
a(24+23) = a(47) = 0, a(48) = 47 is prime.
a(50) = 45 and gcd(45,50) = 5, thus a(51) = 45 - 5 = 40.
a(52) = 39 and gcd(39,52) = 13, thus a(53) = 39 - 13 = 26. Then, a(53+26) = 0 and 79 = a(80) is prime.
MATHEMATICA
FoldList[Abs[#1-GCD[#1, #2]]&, 1, Range@96] (* Ivan N. Ianakiev, Aug 15 2015 *)
PROG
(PARI) print1(a=1); m=1; for(n=1, 199, print1( ", ", a=abs(a-gcd(a, n))))
(Haskell)
a261301 n = a261301_list !! (n-1)
a261301_list = 1 : map abs
(zipWith (-) a261301_list (zipWith gcd [1..] a261301_list))
-- Reinhard Zumkeller, Sep 07 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Aug 14 2015
STATUS
approved