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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)
A062065_list = list(islice(A062065_gen(), 20)) # Chai Wah Wu, Sep 10 2023
CROSSREFS
Sequence in context: A005682 A114833 A065617 * A008936 A320452 A073769
KEYWORD
nonn
AUTHOR
Olivier Gérard, Jun 26 2001
EXTENSIONS
More terms from Naohiro Nomoto, Oct 07 2001
Terms a(27) to a(41) from Klaus Brockhaus, May 17 2003
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)