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A092433
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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.
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10
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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)
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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LoGirl, The game 887, Japanese TV program for junior high and primary school student, Jul 11 2016
Partygamecentral.com, Buzz [broken link]
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FORMULA
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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)))).
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EXAMPLE
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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.
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MAPLE
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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;
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MATHEMATICA
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Select[Range[300], Mod[ #, 7] == 0 || MemberQ[IntegerDigits[ # ], 7] &]
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PROG
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CROSSREFS
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KEYWORD
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base,easy,nonn,changed
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AUTHOR
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Jim Ferry (jferry(AT)uiuc.edu), Mar 23 2004
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STATUS
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approved
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