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

1,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A136992 A089694 A071069 * A018525 A102935 A287210

Adjacent sequences: A116436 A116437 A116438 * A116440 A116441 A116442

Keyword

base,nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

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

Status

approved