A092457 -id:A092457 - cp's OEIS frontend

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

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

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.

			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.

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.

Cf. A008589 (divisible by 7), A011537 (containing digit 7).
Cf. A092451-A092457.
Complement is A376047.

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

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

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

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)))).

A092451 Numbers that either contain the digit 2 or are divisible by 2.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 121

Offset: 0

N. J. A. Sloane, Mar 24 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Cf. A092433, A092452, A092453, A092454, A092455, A092456, A092457.

Select[Range[0,140],DigitCount[#,10,2]>0||Divisible[ #,2]&] (* Harvey P. Dale, Jun 28 2011 *)
Select[Range[0, 300], Mod[#, 2] == 0||MemberQ[IntegerDigits[#], 2] &] (* Vincenzo Librandi, Jul 19 2016 *)

isok(n) = !(n % 2) || vecsearch(vecsort(digits(n,2),,8),2); \\ Michel Marcus, Jul 19 2016

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 25 2004

A092453 Numbers that either contain the digit 4 or are divisible by 4.

Original entry on oeis.org

0, 4, 8, 12, 14, 16, 20, 24, 28, 32, 34, 36, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 52, 54, 56, 60, 64, 68, 72, 74, 76, 80, 84, 88, 92, 94, 96, 100, 104, 108, 112, 114, 116, 120, 124, 128, 132, 134, 136, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 152, 154, 156

Offset: 0

N. J. A. Sloane, Mar 24 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A092433, A092451-A092457.

Select[Range[0, 300], Mod[#, 4] == 0||MemberQ[IntegerDigits[#], 4] &] (* Vincenzo Librandi, Jul 19 2016 *)

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 25 2004

A092456 Numbers that either contain the digit 8 or are divisible by 8.

Original entry on oeis.org

0, 8, 16, 18, 24, 28, 32, 38, 40, 48, 56, 58, 64, 68, 72, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 96, 98, 104, 108, 112, 118, 120, 128, 136, 138, 144, 148, 152, 158, 160, 168, 176, 178, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 192, 198, 200, 208, 216, 218

Offset: 0

N. J. A. Sloane, Mar 24 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A092433, A092451-A092457.

Select[Range[0, 300], Mod[#, 8] == 0||MemberQ[IntegerDigits[#], 8] &] (* Vincenzo Librandi, Jul 19 2016 *)

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 25 2004

Added missing term 188 by Vincenzo Librandi, Jul 19 2016

A092452 Numbers that either contain the digit 3 or are divisible by 3.

Original entry on oeis.org

0, 3, 6, 9, 12, 13, 15, 18, 21, 23, 24, 27, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 45, 48, 51, 53, 54, 57, 60, 63, 66, 69, 72, 73, 75, 78, 81, 83, 84, 87, 90, 93, 96, 99, 102, 103, 105, 108, 111, 113, 114, 117, 120, 123, 126, 129, 130, 131, 132, 133, 134, 135, 136, 137

Offset: 0

N. J. A. Sloane, Mar 24 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Cf. A092433, A092451, A092453, A092454, A092455, A092456, A092457.

Select[Range[0, 150], Mod[#, 3] == 0||MemberQ[IntegerDigits[#], 3] &] (* Vincenzo Librandi, Jul 19 2016 *)

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 25 2004

Added missing term 133 by Vincenzo Librandi, Jul 19 2016

A092454 Numbers that either contain the digit 5 or are divisible by 5.

Original entry on oeis.org

0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210

Offset: 0

N. J. A. Sloane, Mar 24 2004

Cf. A092433, A092451-A092457.

Union[Join[5 Range[100],Select[Range[500],MemberQ[IntegerDigits[#],5]&]]] (* Harvey P. Dale, Dec 08 2010 *)

ll(n)=length(Str(n)) f(n,m)=(n%10^(ll(n)-m) - n%10^(ll(n)-m-1))/10^(ll(n)-m-1) a(n,m)=s=0;for(i=0,ll(n),if(f(n,i)==m,s=s+1,s=s));return(s) for (j=0,300,if(Mod(j,5)==0 || a(j,5)==1,print1(j,",")))

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 25 2004

A092455 Numbers that either contain the digit 6 or are divisible by 6.

Original entry on oeis.org

0, 6, 12, 16, 18, 24, 26, 30, 36, 42, 46, 48, 54, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 76, 78, 84, 86, 90, 96, 102, 106, 108, 114, 116, 120, 126, 132, 136, 138, 144, 146, 150, 156, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 174, 176, 180, 186, 192, 196

Offset: 0

N. J. A. Sloane, Mar 24 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A092433, A092451, A092452, A092453, A092454, A092456, A092457.

Select[Range[0,200],Divisible[#,6]||DigitCount[#,10,6]>0&] (* Harvey P. Dale, Jun 04 2011 *)
Select[Range[0, 300], Mod[#, 6] == 0||MemberQ[IntegerDigits[#], 6] &] (* Vincenzo Librandi, Jul 19 2016 *)

More terms from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 25 2004

Corrected by Harvey P. Dale, Jun 04 2011

cp's OEIS Frontend

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.

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A092451 Numbers that either contain the digit 2 or are divisible by 2.

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A092453 Numbers that either contain the digit 4 or are divisible by 4.

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A092456 Numbers that either contain the digit 8 or are divisible by 8.

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A092452 Numbers that either contain the digit 3 or are divisible by 3.

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A092454 Numbers that either contain the digit 5 or are divisible by 5.

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A092455 Numbers that either contain the digit 6 or are divisible by 6.

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