A358737 - OEIS

%I #43 Jan 04 2023 14:37:16

%S 101,139,53,557,223,31,1117,43,373,59,17,1123,281,5,563,23,47,1129,29,

%T 283,103,7,227,71,379,569,67,163,571,127,13,229,191,37,41,383,1151,3,

%U 1153,577,11,17,89,193,61,43,83,1163,97,233,53,389,73,167,1171,293

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

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

%H Michael De Vlieger, <a href="/A358737/b358737.txt">Table of n, a(n) for n = 1..10000</a>

%H Yann Bugeaud, <a href="https://arxiv.org/abs/1609.07926">On the digital representation of integers with bounded prime factors</a>, Osaka J. Math. 55 (2018), 315-324; arXiv:1609.07926 [math.NT], 2016.

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

%e For n = 2:

%e - A359098(2) = 1112 = 2^3 * 139,

%e - hence a(2) = 139.

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

%o (PARI) { for (n=1, 1172, if (n%10 && #select(d->d, digits(n))==4, f = factor(n); print1 (f[#f~, 1]", "))) }

%o (Python)

%o from itertools import count, islice

%o from sympy import primefactors

%o def A358737_gen(): # generator of terms

%o     for a in count(3):

%o         a10 = 10**a

%o         for ad in range(1,10):

%o             for b in range(2,a):

%o                 b10 = 10**b

%o                 for bd in range(1,10):

%o                     for c in range(1,b):

%o                         c10 = 10**c

%o                         yield from (max(primefactors(ad*a10+bd*b10+cd*c10+dd)) for cd in range(1,10) for dd in range(1,10))

%o A358737_list = list(islice(A358737_gen(),30)) # _Chai Wah Wu_, Jan 04 2023

%Y Cf. A006530, A359098.

%K nonn,base

%O 1,1

%A _Rémy Sigrist_, Jan 04 2023