A092433 Positive numbers from the children's game "Buzz" or "Sevens": positive integers which are divisible by seven, or which contain a seven as a digit.

7, 14, 17, 21, 27, 28, 35, 37, 42, 47, 49, 56, 57, 63, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 84, 87, 91, 97, 98, 105, 107, 112, 117, 119, 126, 127, 133, 137, 140, 147, 154, 157, 161, 167, 168, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 182, 187, 189, 196

Offset: 1

Author

Jim Ferry (jferry(AT)uiuc.edu), Mar 23 2004

Keywords

• base
• easy
• nonn

Comments

Almost all integers are in this sequence: It has asymptotic density 1 since the percentage of n-digit numbers with no digit 7 tends to 0 as n -> oo. - M. F. Hasler, Oct 12 2020

Does not contain 114.

Examples

			7 is the first term, both because it is a multiple of 7 and because it contains a 7. 14 is next, being a multiple of 7. 17 is the third term: it contains a 7.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Darren Gerson, Buzz.
• LoGirl, The game 887, Japanese TV program for junior high and primary school student, Jul 11 2016
• Partygamecentral.com, Buzz [broken link]
• TeachingTips, Academic Games, Buzz.

Crossrefs

Cf. A008589 (divisible by 7), A011537 (containing digit 7).

Cf. A092451-A092457.

Complement is A376047.

Programs

Maple

isA092433 := proc(n)
    if modp(n,7) = 0 then
        true;
    else
        convert(convert(n,base,10),set) ;
        if 7 in % then
            true;
        else
            false;
        end if;
    end if;
end proc:
for n from 1 to 200 do
    if isA092433(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Jul 19 2016

Mathematica

Select[Range[300], Mod[ #, 7] == 0 || MemberQ[IntegerDigits[ # ], 7] &]

PARI

is(n) = n % 7 == 0 || setsearch(Set(digits(n)),7) \\ David A. Corneth, Oct 01 2019, simplified by M. F. Hasler, Oct 12 2020

Formula

Integers n for which the coefficient of x^n is nonzero in x^7 / (1 - x^7) + Sum_{k>=0} x^(7*10^k)*(1 - x^(10^k)) / ((1 - x)*(1 - x^(10^(k+1)))).