A116439 Numbers k which when sandwiched between two 4's give a multiple of k.

1, 2, 4, 11, 13, 14, 22, 26, 28, 44, 52, 77, 91, 137, 146, 274, 292, 548, 9091, 19802, 39604, 909091, 5882353, 10989011, 12987013, 13986014, 15037594, 16194332, 19138756, 21978022, 25974026, 27972028, 30075188, 43956044, 51948052, 52631579, 76923077, 90909091

Offset: 1

Author

Giovanni Resta, Feb 15 2006

Keywords

• base
• nonn

Examples

			91 belongs since 4914 is a multiple of 91 (91*54).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..4735

Crossrefs

Cf. A116436, A116437, A116438, A116440, A116441, A116442, A116443, A116444.

Programs

Mathematica

f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[4, 9] (* Ray Chandler, May 11 2007 *)
Select[Range[52000000],Divisible[FromDigits[Join[{4}, IntegerDigits[#],{4}]],#]&]  (* Harvey P. Dale, Mar 14 2011 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 2, 4]
    for k in count(2):
        t = 4*(10**(k+1) + 1)
        yield from (t//i for i in range(400, 40, -1) if t%i == 0)
print(list(islice(agen(), 38))) # Michael S. Branicky, Mar 26 2023

Extensions

a(36) and beyond from Michael S. Branicky, Mar 26 2023