A376280 Record values in A085908.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 112, 135, 175, 192, 224, 2304, 2625, 4116, 4608, 4704, 5376, 55125, 59049, 74088, 83349, 91125, 95256, 99225, 104976, 1062882, 1306368, 1333584, 1469664, 1492992, 1524096, 1594323, 1679616, 17360406, 21337344, 23914845, 2490394032, 29900390625, 319070390625

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

Formula

a(n) = A085908(A376278(n)).

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

# using A085908 in the form of a list
R:= NULL: m:= 0: count:= 0:
for i from 1 to nops(A085908) do
  if A085908[i] > m then
    count:= count+1; m:= A085908[i];  R:= R, m
  fi
od:
R;

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
A376280_list = list(islice(A376280_gen(), 30)) # Chai Wah Wu, Sep 20 2024

Crossrefs

Cf. A002473, A085908, A376278.

Sequence in context: A250266 A357936 A085908 * A110304 A043315 A044912

Adjacent sequences: A376277 A376278 A376279 * A376281 A376282 A376283

Keyword

nonn,base

Author

Robert Israel, Sep 18 2024

Status

approved