A062294 A B_2 sequence: a(n) is the smallest prime such that the pairwise sums of distinct elements are all distinct.

2, 3, 5, 7, 11, 17, 29, 47, 67, 83, 131, 163, 233, 307, 397, 443, 617, 727, 809, 941, 1063, 1217, 1399, 1487, 1579, 1931, 2029, 2137, 2237, 2659, 2777, 3187, 3659, 3917, 4549, 4877, 5197, 5471, 5981, 6733, 7207, 7349, 8039, 8291, 8543, 9283, 9689, 10037

Offset: 1

Author

Labos Elemer, Jul 02 2001

Keywords

• nonn

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..3600
• Eric Weisstein's World of Mathematics, B2-Sequence
• Index entries for B_2 sequences

Crossrefs

Cf. A011185, A010672, A025582, A005282, A061781, A061784, A062292, A079848, A133096.

Programs

Python

from itertools import islice
from sympy import nextprime
def A062294_gen(): # generator of terms
    aset2, alist, k = set(), [], 0
    while (k:=nextprime(k)):
        bset2 = set()
        for a in alist:
            if (b:=a+k) in aset2:
                break
            bset2.add(b)
        else:
            yield k
            alist.append(k)
            aset2.update(bset2)
A062294_list = list(islice(A062294_gen(),30)) # Chai Wah Wu, Sep 11 2023

Extensions

Edited, corrected and extended by Klaus Brockhaus, Sep 17 2007