A133097 a(n) = A005282(n) - A011185(n-1).

0, 0, 1, 3, 5, 8, 10, 15, 27, 28, 23, 28, 20, 30, 22, 40, 32, 45, 27, 62, 89, 62, 116, 167, 105, 118, 108, 51, 99, 151, 88, 137, 137, 265, 174, 195, 320, 321, 249, 283, 226, 281, 293, 394, 465, 369, 585, 565, 639, 404, 483, 221, 233, 428, 384, 370, 527, 431, 818

Offset

1,4

Comments

Also A025582(n) - A010672(n-1).

A005282 is the sequence of smallest numbers such that the pairwise sums of not necessarily distinct elements are all distinct, whereas A011185 is the sequence of smallest numbers such that the pairwise sums of distinct elements are all distinct.

Sequence has negative terms; the first one is a(65) = -130.

Links

Klaus Brockhaus, Table of n, a(n) for n = 1..2400

Example

a(6) = A005282(6) - A011185(6) = 21 - 13 = 8.

Prog

(Python)
from itertools import count, islice
from collections import deque
def A133097_gen(): # generator of terms
    aset2, alist, bset2, blist, aqueue, bqueue = set(), [], set(), [], deque(), deque()
    for k in count(1):
        cset2 = {k<<1}
        if (k<<1) not in aset2:
            for a in alist:
                if (m:=a+k) in aset2:
                    break
                cset2.add(m)
            else:
                aqueue.append(k)
                alist.append(k)
                aset2.update(cset2)
        cset2 = set()
        for b in blist:
            if (m:=b+k) in bset2:
                break
            cset2.add(m)
        else:
            bqueue.append(k)
            blist.append(k)
            bset2.update(cset2)
        if len(aqueue) > 0 and len(bqueue) > 0:
            yield aqueue.popleft()-bqueue.popleft()
A133097_list = list(islice(A133097_gen(), 30)) # Chai Wah Wu, Sep 11 2023

Crossrefs

Cf. A005282, A011185, A025582, A010672, A133096.

Sequence in context: A182082 A117467 A310025 * A117176 A212987 A217919

Adjacent sequences: A133094 A133095 A133096 * A133098 A133099 A133100

Keyword

sign

Author

Klaus Brockhaus, Sep 17 2007

Status

approved