A376278 Positions of records in A085908.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 17, 19, 22, 23, 26, 41, 46, 47, 53, 55, 59, 74, 83, 91, 95, 99, 104, 106, 130, 133, 146, 149, 152, 159, 167, 173, 213, 239, 249, 299, 319, 383, 454, 467, 545, 613, 623, 636, 641, 646, 698, 916, 931, 1173, 1197, 1222, 1257, 1642, 1650, 1676, 1760, 1825, 1916

Offset

1,2

Comments

Numbers k such that for 1 <= j < k, the least 7-smooth number that starts with j is less than the least 7-smooth number that starts with k.

Record values are in A376280.

Links

Robert Israel, Table of n, a(n) for n = 1..207

Formula

A376280(n) = A085908(a(n)).

Example

a(12) = 13 is a term because the least 7-smooth number starting with 13 is A085908(13) = 135 = 3^2 * 5 * 7, while A085908(j) < 135 for j < 13.

Maple

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

Prog

(Python)
from itertools import count, islice
def A376278_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 n
            c = kmax
A376278_list = list(islice(A376278_gen(), 30)) # Chai Wah Wu, Sep 20 2024

Crossrefs

Cf. A085908, A376280.

Sequence in context: A332166 A017904 A368902 * A143290 A272038 A044961

Adjacent sequences: A376275 A376276 A376277 * A376279 A376280 A376281

Keyword

nonn,base

Author

Robert Israel, Sep 18 2024

Status

approved