OFFSET
1,5
COMMENTS
a(n) represents the partition size generated by greedy algorithm at A276380(n) such that all parts k are unique and in A003586.
See A276380 for further comments about the greedy algorithm.
Row n = 1 for n that are in A003586.
REFERENCES
V. Dimitrov, G. Jullien, and R. Muscedere, Multiple Number Base System Theory and Applications, 2nd ed., CRC Press, 2012, pp. 35-39.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
a(n) Terms k in row n of A276380:
1 1
1 2
1 3
1 4
2 1,4
1 6
2 1,6
1 8
1 9
2 1,9
2 2,9
1 12
2 1,12
2 2,12
2 3,12
1 16
2 1,16
1 18
2 1,18
2 2,18
2 3,18
2 4,18
3 1,4,18
...
MATHEMATICA
Table[Length@ DeleteCases[Append[Abs@ Differences@ #, Last@ #], k_ /; k == 0] &@ NestWhileList[# - SelectFirst[# - Range[0, # - 1], Block[{m = #, n = 6}, While[And[m != 1, ! CoprimeQ[m, n]], n = GCD[m, n]; m = m/n]; m == 1] &] &, n, # > 1 &], {n, 100}]
PROG
(Python)
from itertools import count, takewhile
N = 100
def B(p): return list(takewhile(lambda x: x<=N, (p**i for i in count(0))))
B23set = set(b*t for b in B(2) for t in B(3) if b*t <= N)
B23lst = sorted(B23set, reverse=True)
def a(n):
if n in B23set: return 1
big = next(t for t in B23lst if t <= n)
return a(n - big) + 1
print([a(n) for n in range(1, N+1)]) # Michael S. Branicky, Sep 14 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Sep 27 2016
STATUS
approved