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

1,1

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.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A005282, A011185, A133605.

Sequence in context: A337762 A055876 A065847 * A262345 A192149 A115778

Adjacent sequences: A133601 A133602 A133603 * A133605 A133606 A133607

Keyword

nonn

Author

Klaus Brockhaus, Sep 18 2007

Status

approved