OFFSET
1,2
COMMENTS
This is the B3-sequence analog of the Mian-Chowla B2-sequence (A005282): Let a(1)=1; then use the greedy algorithm to choose the smallest a(n) > a(n-1) such that all sums a(i) + a(j) + a(k) are distinct for 1 <= i <= j <= k <= n. The reciprocal sum of the sequence for the first forty terms is 1.837412....
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..176
Eric Weisstein's World of Mathematics, B2-Sequence.
Eric Weisstein's World of Mathematics, Mian-Chowla Sequence.
FORMULA
a(n) = A051912(n-1) + 1. - Peter Kagey, Oct 20 2021
PROG
(Python)
from itertools import count, islice
def A096772_gen(): # generator of terms
aset1, aset2, aset3, alist = set(), set(), set(), []
for k in count(1):
bset2, bset3 = {k<<1}, {3*k}
if 3*k not in aset3:
for d in aset1:
if (m:=d+(k<<1)) in aset3:
break
bset2.add(d+k)
bset3.add(m)
else:
for d in aset2:
if (m:=d+k) in aset3:
break
bset3.add(m)
else:
yield k
alist.append(k)
aset1.add(k)
aset2 |= bset2
aset3 |= bset3
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Aug 15 2004
STATUS
approved