|
|
A062065
|
|
a(1) = 1; for n >= 1, a(n+1) is smallest number such that the sums of any one, two or three of a(1), ..., a(n) are distinct (repetitions not allowed).
|
|
3
|
|
|
1, 2, 4, 8, 15, 28, 52, 96, 165, 278, 460, 663, 980, 1332, 1864, 2609, 3375, 4769, 5600, 6776, 9141, 11505, 14453, 17404, 21904, 25023, 31159, 35006, 42780, 51792, 55799, 68834, 75036, 87163, 96746, 116231, 128924, 144085, 172606, 193507, 207826
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
EXAMPLE
|
1,2,1+2 are different so a(2) = 2; 1,2,3,1+2,1+3,2+3,1+2+3 are not all different (3 = 1+2) so a(3) is not 3; 1,2,4,1+2,1+4,2+4,1+2+4 are all different so a(3) = 4.
|
|
PROG
|
(PARI)
{unique(v)=local(b); b=1; for(j=2, length(v), if(v[j-1]==v[j], b=0)); b}
{news(v, q)=local(s); s=[]; for(i=1, length(v), s=concat(s, v[i]+q)); s}
{m=210000; print1(p=1, ", "); w1=[p]; w2=[]; w3=[]; q=p+1; while(q<m, y1=concat(w1, q); y2=concat(w2, news(w1, q)); y3=concat(w3, news(w2, q)); if(unique(vecsort(concat(concat(y1, y2), y3))), w1=y1; w2=y2; w3=y3; print1(q, ", ")); q=q+1)} \\ Klaus Brockhaus, May 17 2003
(Python)
from itertools import count, islice
def A062065_gen(): # generator of terms
aset2, aset3, alist = set(), set(), [1]
yield 1
for k in count(2):
bset2, bset3 = set(), set()
if not (k in aset2 or k in aset3):
for a in alist:
if (b2:=a+k) in aset2 or b2 in aset3:
break
bset2.add(b2)
else:
for a2 in aset2:
if (b3:=a2+k) in aset2 or b3 in aset3:
break
bset3.add(b3)
else:
yield k
alist.append(k)
aset2.update(bset2)
aset3.update(bset3)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|