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).

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

Offset: 1

Author

Olivier Gérard, Jun 26 2001

Keywords

• nonn

Examples

			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.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..230

Crossrefs

Cf. A036241, A051912.

Programs

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(qKlaus 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

Extensions

More terms from Naohiro Nomoto, Oct 07 2001

Terms a(27) to a(41) from Klaus Brockhaus, May 17 2003