A133744 a(n) = A062295(n) - A133743(n).

0, 0, 0, 0, 0, 0, 15, -19, -44, 0, 31, 33, 80, 43, 92, 0, 112, 305, 140, -77, 336, 261, 0, -103, -228, 129, 131, 268, 429, 292, -153, -805, -352, 189, 985, 2040, 1260, 440, -693, -468, 239, -2367, -1365, -285, 885, 596, 3531, 2608, 3360, 2752, -2196, 0, 2709, 4367, 4411, 2105

Offset

1,7

Comments

A062295 is the sequence of smallest squares such that the pairwise sums of not necessarily distinct elements are all distinct, whereas A133743 is the sequence of smallest squares such that the pairwise sums of distinct elements are all distinct.

Links

Klaus Brockhaus, Table of n, a(n) for n = 1..4944

Example

a(7) = A062295(7) - A133743(7) = 64 - 49 = 15.

Prog

(Python)
from collections import deque
from itertools import count, islice
def A133744_gen(): # generator of terms
    aset2, alist, bset2, blist, aqueue, bqueue = set(), [], set(), [], deque(), deque()
    for k in (n**2 for n 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()
A133744_list = list(islice(A133744_gen(), 30)) # Chai Wah Wu, Sep 11 2023

Crossrefs

Cf. A062295, A133743, A133745.

Sequence in context: A169728 A167054 A241680 * A031112 A219394 A330522

Adjacent sequences: A133741 A133742 A133743 * A133745 A133746 A133747

Keyword

sign

Author

Klaus Brockhaus, Sep 24 2007

Status

approved