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

Author

Rémy Sigrist, Jan 04 2023

Keywords

• nonn
• base

Comments

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

Examples

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

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.

Crossrefs

Cf. A006530, A359098.

Programs

Mathematica

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

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

Formula

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