A084334 a(1) = 1; a(n+1) is the least squarefree m not already used such that |m-a(n)| is not equal to |a(k+1)-a(k)| for any k < n.

1, 2, 5, 3, 7, 13, 6, 11, 19, 10, 21, 31, 14, 26, 39, 15, 29, 47, 17, 33, 53, 22, 37, 58, 23, 42, 65, 38, 66, 30, 55, 77, 34, 67, 35, 61, 95, 41, 70, 107, 43, 82, 122, 46, 87, 129, 51, 89, 133, 59, 105, 57, 102, 149, 62, 111, 161, 69, 127, 71, 123, 174, 73, 130, 183, 74

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 18 2003

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A081145, A084331.

Programs

Maple

N:= 1000: # for terms before the first term > N
A[1]:= 1:
SF:= select(numtheory:-issqrfree, [$2..N]):
DA:= {}:
y:= 1:
found:= true:
for n from 2 while found do
  found:= false;
  for j from 1 to nops(SF) while not found do
    x:= SF[j];
    if not member(abs(x-y),DA) then
       found:= true;
       A[n]:= x;
       DA:= DA union {abs(x-y)};
       SF:= subsop(j=NULL, SF);
       y:= x;
    fi
od od:
convert(A,list); # Robert Israel, Feb 22 2024

Extensions

Edited and extended by David Wasserman, Dec 15 2004