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A285802 Smallest number that when multiplied by n contains the digit 7. 1
7, 35, 9, 18, 14, 12, 1, 9, 3, 7, 7, 6, 6, 5, 5, 11, 1, 4, 3, 35, 7, 8, 9, 3, 3, 3, 1, 17, 3, 9, 7, 18, 9, 5, 2, 2, 1, 2, 2, 18, 7, 9, 4, 4, 6, 6, 1, 12, 3, 14, 7, 11, 7, 5, 5, 12, 1, 3, 3, 12, 7, 6, 6, 9, 11, 11, 1, 4, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: 35 is the highest value to occur in this sequence.

Conjecture is true. First of all we notice that a(10*k) = a(k), so we can consider only numbers not ending in 0. Then, it is easy to verify that for any number k between 1 and 99 not ending in 0, there is a multiple of k not larger than 35*k which has a 7 in one the two last digits. Since the last two digits of the products only depend on the last two digits of k, this extends immediately to larger numbers. - Giovanni Resta, Apr 27 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(2) = 35 because no even number ends in 7, but we can have even numbers whose next-to-last digit is 7; the smallest number is 70, which is even, and 2 times 35 is 70.

MAPLE

f:= proc(n) local k;

  for k from 1 do

    if has(convert(n*k, base, 10), 7) then return k fi

  od

end proc:

map(f, [$1..100]); # Robert Israel, Nov 26 2019

MATHEMATICA

Table[k = 1; While[DigitCount[k n, 10, 7] == 0, k++]; k, {n, 82}] (* Michael De Vlieger, Apr 26 2017 *)

PROG

(Python)

def a(n):

    k=1

    while True:

        if "7" in str(n*k): return k

        k+=1

print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Apr 27 2017

(PARI) a(n) = {my(k=1); while(!vecsearch(vecsort(digits(n*k)), 7), k++); k; } \\ Michel Marcus, Jun 09 2018

CROSSREFS

Sequence in context: A196968 A000829 A247158 * A340523 A061825 A077536

Adjacent sequences:  A285799 A285800 A285801 * A285803 A285804 A285805

KEYWORD

nonn,base,easy,look

AUTHOR

J. Lowell, Apr 26 2017

STATUS

approved

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Last modified July 28 03:49 EDT 2021. Contains 346316 sequences. (Running on oeis4.)