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

1,1

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

Prog

(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

Crossrefs

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

Sequence in context: A113192 A077673 A071255 * A245879 A113016 A085136

Adjacent sequences: A062291 A062292 A062293 * A062295 A062296 A062297

Keyword

nonn,changed

Author

Labos Elemer, Jul 02 2001

Extensions

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

Status

approved