%I #20 Sep 20 2024 23:55:09
%S 1,2,3,4,5,6,7,8,9,10,112,135,175,192,224,2304,2625,4116,4608,4704,
%T 5376,55125,59049,74088,83349,91125,95256,99225,104976,1062882,
%U 1306368,1333584,1469664,1492992,1524096,1594323,1679616,17360406,21337344,23914845,2490394032,29900390625,319070390625
%N Record values in A085908.
%C 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.
%C Positions of records are in A376278.
%H Robert Israel, <a href="/A376280/b376280.txt">Table of n, a(n) for n = 1..207</a>
%F a(n) = A085908(A376278(n)).
%e 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.
%p # using A085908 in the form of a list
%p R:= NULL: m:= 0: count:= 0:
%p for i from 1 to nops(A085908) do
%p if A085908[i] > m then
%p count:= count+1; m:= A085908[i]; R:= R, m
%p fi
%p od:
%p R;
%o (Python)
%o from itertools import count, islice
%o def A376280_gen(): # generator of terms
%o def f(x):
%o c = 0
%o i7 = 1
%o m = x
%o for i in count(0):
%o if i7 > x:
%o break
%o j5 = 1
%o r = m
%o for j in count(0):
%o if j5 > m:
%o break
%o k3 = 1
%o t = r
%o for k in count(0):
%o if k3 > r:
%o break
%o c += t.bit_length()
%o k3 *= 3
%o t //= 3
%o j5 *= 5
%o r //= 5
%o i7 *= 7
%o m //= 7
%o return c
%o c = 1
%o yield 1
%o for n in count(2):
%o for l in count(0):
%o kmin, kmax = n*10**l-1, (n+1)*10**l-1
%o mmin, mmax = f(kmin), f(kmax)
%o if mmax>mmin:
%o while kmax-kmin > 1:
%o kmid = kmax+kmin>>1
%o mmid = f(kmid)
%o if mmid > mmin:
%o kmax, mmax = kmid, mmid
%o else:
%o kmin, mmin = kmid, mmid
%o break
%o if kmax > c:
%o yield kmax
%o c = kmax
%o A376280_list = list(islice(A376280_gen(),30)) # _Chai Wah Wu_, Sep 20 2024
%Y Cf. A002473, A085908, A376278.
%K nonn,base
%O 1,2
%A _Robert Israel_, Sep 18 2024