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

Author

Klaus Brockhaus, Sep 17 2007

Keywords

• sign

Comments

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.

Examples

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

Links

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

Crossrefs

Cf. A062294, A079848, A133097.

Programs

Python

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