A358737 a(n) is the greatest prime number dividing A359098(n).

101, 139, 53, 557, 223, 31, 1117, 43, 373, 59, 17, 1123, 281, 5, 563, 23, 47, 1129, 29, 283, 103, 7, 227, 71, 379, 569, 67, 163, 571, 127, 13, 229, 191, 37, 41, 383, 1151, 3, 1153, 577, 11, 17, 89, 193, 61, 43, 83, 1163, 97, 233, 53, 389, 73, 167, 1171, 293

Offset

1,1

Comments

Bugeaud proves that a(n) tends to infinity as n tends to infinity.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Yann Bugeaud, On the digital representation of integers with bounded prime factors, Osaka J. Math. 55 (2018), 315-324; arXiv:1609.07926 [math.NT], 2016.

Formula

a(n) = A006530(A359098(n)).

Example

For n = 2:
- A359098(2) = 1112 = 2^3 * 139,
- hence a(2) = 139.

Mathematica

Map[FactorInteger[#][[-1, 1]] &, Select[Range[1111, 1172], And[Mod[#, 10] != 0, Total@ Most@ DigitCount[#] == 4] &]] (* Michael De Vlieger, Jan 04 2023 *)

Prog

(PARI) { for (n=1, 1172, if (n%10 && #select(d->d, digits(n))==4, f = factor(n); print1 (f[#f~, 1]", "))) }
(Python)
from itertools import count, islice
from sympy import primefactors
def A358737_gen(): # generator of terms
    for a in count(3):
        a10 = 10**a
        for ad in range(1, 10):
            for b in range(2, a):
                b10 = 10**b
                for bd in range(1, 10):
                    for c in range(1, b):
                        c10 = 10**c
                        yield from (max(primefactors(ad*a10+bd*b10+cd*c10+dd)) for cd in range(1, 10) for dd in range(1, 10))
A358737_list = list(islice(A358737_gen(), 30)) # Chai Wah Wu, Jan 04 2023

Crossrefs

Cf. A006530, A359098.

Sequence in context: A162463 A035790 A139489 * A106994 A050672 A122531

Adjacent sequences: A358734 A358735 A358736 * A358738 A358739 A358740

Keyword

nonn,base

Author

Rémy Sigrist, Jan 04 2023

Status

approved