A133604 Elements of A005282 that are also the sum of a pair of not necessarily distinct elements of A005282.

2, 4, 8, 21, 66, 97, 204, 565, 662, 775, 970, 1821, 2780, 6374, 8730, 8942, 10898, 24596, 55307, 67189, 79047, 84345, 164868, 231694, 233570, 234619, 271511, 298414, 433973, 474668, 475800, 567408, 829129, 839728, 889285, 1394240

Offset: 1

Author

Klaus Brockhaus, Sep 18 2007

Keywords

• nonn

Comments

A005282 is the sequence of smallest numbers such that the pairwise sums of not necessarily distinct elements are all distinct.

Conjecture: 2, 4 and 8 are the only terms n such that n = 2*A005282(k) for some k.

Examples

			A005282(3) = 4 + 4 = 8 = A005282(4), hence 8 is in the sequence.
A005282(10) = 81, A005282(12) = 123. 81 + 123 = 204 = A005282(15), hence 204 is in the sequence.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..98

Crossrefs

Cf. A005282, A011185, A133605.

Programs

Python

from itertools import count, islice
def A133604_gen(): # generator of terms
    aset2, alist = set(), []
    for k in count(1):
        bset2 = {r:=k<<1}
        if r not in aset2:
            for d in alist:
                if (m:=d+k) in aset2:
                    break
                bset2.add(m)
            else:
                if k in aset2:
                    yield k
                alist.append(k)
                aset2.update(bset2)
A133604_list = list(islice(A133604_gen(),30)) # Chai Wah Wu, Sep 11 2023