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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. 10
 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 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 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. TeachingTips, Academic Games. 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)))). 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] &] PROG (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 CROSSREFS Cf. A008589 (divisible by 7), A011537 (containing digit 7). 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 December 3 19:10 EST 2023. Contains 367540 sequences. (Running on oeis4.)