A062294 -id:A062294 - cp's OEIS frontend

A133096 a(n) = A079848(n) - A062294(n).

0, 0, 0, 4, 12, 20, 18, 50, 34, 66, 80, 70, 120, 76, 90, 198, 140, 70, 110, 156, 100, 164, 10, -6, 198, 66, 258, 280, 732, 390, 594, 342, 270, 314, 210, 402, 252, 246, -28, -204, -224, 234, 14, 528, 500, 850, 1110, 942, 1014, 1542, 1906, 1416, 1034, 1454, 970, 982, 1518

Offset: 1

Klaus Brockhaus, Sep 17 2007

sign

A079848 is the sequence of smallest primes such that the pairwise sums of not necessarily distinct elements are all distinct, whereas A062294 is the sequence of smallest primes such that the pairwise sums of distinct elements are all distinct.

			a(6) = A079848(6) - A062294(6) = 37 - 17 = 20.

Klaus Brockhaus, Table of n, a(n) for n = 1..3600

Cf. A062294, A079848, A133097.

from collections import deque
from itertools import islice
from sympy import nextprime
def A133096_gen(): # generator of terms
    aset2, alist, bset2, blist, aqueue, bqueue, k = set(), [], set(), [], deque(), deque(), 1
    while (k:=nextprime(k)):
        cset2 = set()
        for a in alist:
            if (m:=k-a) 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()
A133096_list = list(islice(A133096_gen(),30)) # Chai Wah Wu, Sep 11 2023

A062292 A B_2 sequence: a(n) is the smallest cube such that the pairwise sums of {a(1)...a(n)} are all distinct.

Original entry on oeis.org

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 2197, 2744, 3375, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 35937, 42875, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 85184, 91125, 97336

Offset: 1

Labos Elemer, Jul 02 2001

nonn

A Mian-Chowla sequence consisting only of cubes.

			During recursive construction of this set, for n=1-50, the cubes of 12,18,24,32,34,36,48 are left out to keep all sums of distinct cubes distinct from each other.

Cf. A011185, A010672, A025582, A005282, A062294.

from itertools import count, islice
def A062292_gen(): # generator of terms
    aset1, aset2, alist = set(), set(), []
    for k in (n**3 for n in count(1)):
        bset2 = {k<<1}
        if (k<<1) not in aset2:
            for d in aset1:
                if (m:=d+k) in aset2:
                    break
                bset2.add(m)
            else:
                yield k
                alist.append(k)
                aset1.add(k)
                aset2.update(bset2)
A062292_list = list(islice(A062292_gen(),30)) # Chai Wah Wu, Sep 05 2023

cp's OEIS Frontend

A133096 a(n) = A079848(n) - A062294(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python