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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).

%I A062065 #21 Sep 12 2023 02:04:24
%S A062065 1,2,4,8,15,28,52,96,165,278,460,663,980,1332,1864,2609,3375,4769,
%T A062065 5600,6776,9141,11505,14453,17404,21904,25023,31159,35006,42780,51792,
%U A062065 55799,68834,75036,87163,96746,116231,128924,144085,172606,193507,207826
%N 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).
%H A062065 Chai Wah Wu, <a href="/A062065/b062065.txt">Table of n, a(n) for n = 1..230</a>
%e A062065 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.
%o A062065 (PARI)
%o A062065 {unique(v)=local(b); b=1; for(j=2,length(v),if(v[j-1]==v[j],b=0)); b}
%o A062065 {news(v,q)=local(s); s=[]; for(i=1,length(v),s=concat(s,v[i]+q)); s}
%o A062065 {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
%o A062065 (Python)
%o A062065 from itertools import count, islice
%o A062065 def A062065_gen(): # generator of terms
%o A062065     aset2, aset3, alist = set(), set(), [1]
%o A062065     yield 1
%o A062065     for k in count(2):
%o A062065         bset2, bset3 = set(), set()
%o A062065         if not (k in aset2 or k in aset3):
%o A062065             for a in alist:
%o A062065                 if (b2:=a+k) in aset2 or b2 in aset3:
%o A062065                     break
%o A062065                 bset2.add(b2)
%o A062065             else:
%o A062065                 for a2 in aset2:
%o A062065                     if (b3:=a2+k) in aset2 or b3 in aset3:
%o A062065                         break
%o A062065                     bset3.add(b3)
%o A062065                 else:
%o A062065                     yield k
%o A062065                     alist.append(k)
%o A062065                     aset2.update(bset2)
%o A062065                     aset3.update(bset3)
%o A062065 A062065_list = list(islice(A062065_gen(),20)) # _Chai Wah Wu_, Sep 10 2023
%Y A062065 Cf. A036241, A051912.
%K A062065 nonn
%O A062065 1,2
%A A062065 _Olivier Gérard_, Jun 26 2001
%E A062065 More terms from _Naohiro Nomoto_, Oct 07 2001
%E A062065 Terms a(27) to a(41) from _Klaus Brockhaus_, May 17 2003