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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..60.

Darren Gerson, Buzz.

LoGirl, The game 887, Japanese TV program for junior high and primary school student, Jul 11 2016

Partygamecentral.com, Buzz.

TeachingTips, Academic Games.

FORMULA

Integers n for which the coefficient of x^n is nonzero in x^7 / (1 - x^7) + sum(x^(7 10^k) (1 - x^(10^k)) / ((1 - x) (1 - x^(10^(k+1)))), k=0 to infinity).

EXAMPLE

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.

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] &]

CROSSREFS

Cf. A092451-A092457.

Sequence in context: A118905 A254064 A257224 * A056203 A178732 A025021

Adjacent sequences:  A092430 A092431 A092432 * A092434 A092435 A092436

KEYWORD

base,easy,nonn

AUTHOR

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

STATUS

approved

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Last modified February 22 15:52 EST 2019. Contains 320399 sequences. (Running on oeis4.)