

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
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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. A092451A092457.
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



