OFFSET
1,2
COMMENTS
Numbers m that m is the least 7-smooth number that starts with some k, such that for all j < k there is a 7-smooth number < m that starts with j.
Positions of records are in A376278.
LINKS
Robert Israel, Table of n, a(n) for n = 1..207
EXAMPLE
a(12) = 135 because 135 is the least 7-smooth number that starts with 13, and for every j < 13 there is a 7-smooth number less than 135 starting with j.
MAPLE
PROG
(Python)
from itertools import count, islice
def A376280_gen(): # generator of terms
def f(x):
c = 0
i7 = 1
m = x
for i in count(0):
if i7 > x:
break
j5 = 1
r = m
for j in count(0):
if j5 > m:
break
k3 = 1
t = r
for k in count(0):
if k3 > r:
break
c += t.bit_length()
k3 *= 3
t //= 3
j5 *= 5
r //= 5
i7 *= 7
m //= 7
return c
c = 1
yield 1
for n in count(2):
for l in count(0):
kmin, kmax = n*10**l-1, (n+1)*10**l-1
mmin, mmax = f(kmin), f(kmax)
if mmax>mmin:
while kmax-kmin > 1:
kmid = kmax+kmin>>1
mmid = f(kmid)
if mmid > mmin:
kmax, mmax = kmid, mmid
else:
kmin, mmin = kmid, mmid
break
if kmax > c:
yield kmax
c = kmax
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robert Israel, Sep 18 2024
STATUS
approved