cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 29 results. Next

A121027 Multiples of 7 containing a 7 in their decimal representation.

Original entry on oeis.org

7, 70, 77, 147, 175, 217, 273, 287, 357, 371, 378, 427, 476, 497, 567, 574, 637, 672, 679, 700, 707, 714, 721, 728, 735, 742, 749, 756, 763, 770, 777, 784, 791, 798, 847, 875, 917, 973, 987, 1057, 1071, 1078, 1127, 1176, 1197, 1267, 1274, 1337, 1372, 1379
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 21 2006

Keywords

Links

Crossrefs

Intersection of A008589 and A011537.
Cf. A121041, A011531, A121022, A121023, A121024, A121025, A121026, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040.

Programs

  • Mathematica
    Select[7*Range[500], MemberQ[IntegerDigits[#], 7] &] (* Paolo Xausa, Feb 25 2024 *)
  • PARI
    is(n)=n%7==0 && setsearch(Set(digits(n)), 7) \\ Charles R Greathouse IV, Feb 12 2017

Formula

a(n) ~ 7n. - Charles R Greathouse IV, Feb 12 2017

Extensions

Typo in comment fixed by Reinhard Zumkeller, May 01 2011

A011532 Numbers that contain a 2.

Original entry on oeis.org

2, 12, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 42, 52, 62, 72, 82, 92, 102, 112, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 142, 152, 162, 172, 182, 192, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Numbers that contain a digit k: A011531 (k=1), A011533 (k=3), A011534 (k=4), A011535 (k=5), A011536 (k=6), A011537 (k=7), A011538 (k=8), A011539 (k=9), A011540 (k=0).

Programs

  • GAP
    Filtered([1..220],n->2 in ListOfDigits(n)); # Muniru A Asiru, Feb 23 2019
  • Haskell
    a011532 n = a011532_list !! (n-1)
a011532_list = filter ((elem '2') . show) [0..]
-- Reinhard Zumkeller, Apr 10 2015
  • Magma
    [n: n in [0..500] | 2 in Intseq(n)]; // Vincenzo Librandi, Jan 11 2016
  • Mathematica
    Select[Range[600] - 1, DigitCount[#, 10, 2]>0 &] (* Vincenzo Librandi, Jan 11 2016 *)

Formula

a(n) ~ n. - Charles R Greathouse IV, Feb 12 2017

A011533 Numbers that contain a 3.

Original entry on oeis.org

3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93, 103, 113, 123, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 153, 163, 173, 183, 193, 203, 213, 223, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 243, 253
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Complement: A052405.
Cf. A016189.
Numbers that contain a digit k: A011531 (k=1), A011532 (k=2), A011534 (k=4), A011535 (k=5), A011536 (k=6), A011537 (k=7), A011538 (k=8), A011539 (k=9), A011540 (k=0).

Programs

  • GAP
    Filtered([1..260],n->3 in ListOfDigits(n)); # Muniru A Asiru, Feb 23 2019
  • Haskell
    a011533 n = a011533_list !! (n-1)
a011533_list = filter ((elem '3') . show) [0..]
-- Reinhard Zumkeller, Apr 10 2015
  • Magma
    [n: n in [0..500] | 3 in Intseq(n)]; // Vincenzo Librandi, Jan 11 2016
  • Maple
    M:= 3: # to get all terms of up to M digits
B:= {3}: A:= {3}:
for i from 2 to M do
   B:= map(t -> seq(10*t+j,j=0..9),B) union
      {seq(10*x+3,x=10^(i-2)..10^(i-1)-1)}:
   A:= A union B;
od:
sort(convert(A,list));# Robert Israel, Jan 11 2016
  • Mathematica
    Select[Range[600] - 1, DigitCount[#, 10, 3]>0 &] (* Vincenzo Librandi, Jan 11 2016 *)
  • PARI
    isok(n)=my(d=digits(n)); for (k=1, #d, if (d[k] == 3, return (1))); \\ Michel Marcus, Jan 11 2016

Formula

a(n) ~ n. - Charles R Greathouse IV, Aug 28 2012
For m >= 1, a(10^m - 9^m) = 10^m-7, a(10^m - 9^m + 1) = 10^m + 3. - Robert Israel, Jan 11 2016

A011534 Numbers that contain a 4.

Original entry on oeis.org

4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, 94, 104, 114, 124, 134, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154, 164, 174, 184, 194, 204, 214, 224, 234, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 254
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Numbers that contain a digit k: A011531 (k=1), A011532 (k=2), A011533 (k=3), A011535 (k=5), A011536 (k=6), A011537 (k=7), A011538 (k=8), A011539 (k=9), A011540 (k=0).

Programs

Formula

a(n) ~ n. - Charles R Greathouse IV, Feb 12 2017

A293869 Square array whose n-th row lists all numbers having n as a substring, n >= 1; read by falling antidiagonals.

Original entry on oeis.org

1, 10, 2, 11, 12, 3, 12, 20, 13, 4, 13, 21, 23, 14, 5, 14, 22, 30, 24, 15, 6, 15, 23, 31, 34, 25, 16, 7, 16, 24, 32, 40, 35, 26, 17, 8, 17, 25, 33, 41, 45, 36, 27, 18, 9, 18, 26, 34, 42, 50, 46, 37, 28, 19, 10, 19, 27, 35, 43, 51, 56, 47, 38, 29, 100, 11
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Examples

			The array starts:
   [ 1  10  11  12  13  14  15  16  17  18  19  21  31 ...] = A011531
   [ 2  12  20  21  22  23  24  25  26  27  28  29  32 ...] = A011532
   [ 3  13  23  30  31  32  33  34  35  36  37  38  39 ...] = A011533
   [ 4  14  24  34  40  41  42  43  44  45  46  47  48 ...] = A011534
   [ 5  15  25  35  45  50  51  52  53  54  55  56  57 ...] = A011535
   [ 6  16  26  36  46  56  60  61  62  63  64  65  66 ...] = A011536
   [ 7  17  27  37  47  57  67  70  71  72  73  74  75 ...] = A011537
   [ 8  18  28  38  48  58  68  78  80  81  82  83  84 ...] = A011538
   [ 9  19  29  39  49  59  69  79  89  90  91  92  93 ...] = A011539
   [10 100 101 102 103 104 105 106 107 108 109 110 210 ...] = A293870
   [11 110 111 112 113 114 115 116 117 118 119 211 311 ...] = A293871
   [12 112 120 121 122 123 124 125 126 127 128 129 212 ...] = A293872
   [   ...             ...             ...             ...]

Links

Crossrefs

Cf. A072484, A292690 (variant starting with row 0).
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539, A293870, A293871, A293872.
Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040.
Cf. A179239, A261370.
Cf. A292451, A292731 (both partially coincide with row 11, but no inclusion relation holds).

Programs

  • Mathematica
    Block[{d = 15, q, a, s}, a = Table[q = n-1; s = IntegerString[n]; Table[While[StringFreeQ[IntegerString[++q], s]]; q, d-n+1], {n, d}]; Table[a[[n, k-n+1]], {k, d}, {n, k}]] (* Paolo Xausa, Mar 01 2024 *)
  • PARI
    has=(n,p,m=10^#Str(p))->until(p>n\=10,n%m==p&&return(1))
Mat(vectorv(12,n,a=[];for(k=n,oo,has(k,n)||next;a=concat(a,k);#a>12&&break);a))
  • Perl
    See Links section.

Formula

T(n, k) = A072484(n, k) for any n > 0 and k = 1..n. - Rémy Sigrist, Jan 29 2021

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

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
Does not contain 114.

Examples

			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.

Links

Crossrefs

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

Programs

  • 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] &]
  • 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

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)))).

A292690 Square array whose n-th row lists all numbers having n as a substring, read by falling antidiagonals, n >= 0.

Original entry on oeis.org

0, 10, 1, 20, 10, 2, 30, 11, 12, 3, 40, 12, 20, 13, 4, 50, 13, 21, 23, 14, 5, 60, 14, 22, 30, 24, 15, 6, 70, 15, 23, 31, 34, 25, 16, 7, 80, 16, 24, 32, 40, 35, 26, 17, 8, 90, 17, 25, 33, 41, 45, 36, 27, 18, 9, 100, 18, 26, 34, 42, 50, 46, 37, 28, 19, 10
Offset: 0

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

This array starts with row 0, see A293869 for the variant which starts with row 1.

Examples

			The array starts:
   [ 0  10  20  30  40  50  60  70  80  90 100 101 102 ...] = A011540
   [ 1  10  11  12  13  14  15  16  17  18  19  21  31 ...] = A011531
   [ 2  12  20  21  22  23  24  25  26  27  28  29  32 ...] = A011532
   [ 3  13  23  30  31  32  33  34  35  36  37  38  39 ...] = A011533
   [ 4  14  24  34  40  41  42  43  44  45  46  47  48 ...] = A011534
   [ 5  15  25  35  45  50  51  52  53  54  55  56  57 ...] = A011535
   [ 6  16  26  36  46  56  60  61  62  63  64  65  66 ...] = A011536
   [ 7  17  27  37  47  57  67  70  71  72  73  74  75 ...] = A011537
   [ 8  18  28  38  48  58  68  78  80  81  82  83  84 ...] = A011538
   [ 9  19  29  39  49  59  69  79  89  90  91  92  93 ...] = A011539
   [10 100 101 102 103 104 105 106 107 108 109 110 210 ...] = A293870
   [11 110 111 112 113 114 115 116 117 118 119 211 311 ...] = A293871
   [12 112 120 121 122 123 124 125 126 127 128 129 212 ...] = A293872
   [   ...             ...             ...             ...]

Links

Crossrefs

Cf. A293869.
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: rows 0 - 9.
Cf. A293870, A293871, A293872, A293873, A293874, A293875, A293876, A293877, A293878, A293879, A293880: rows 10 .. 20.
Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040: subsequences of the above, only multiples of the pattern p.

Programs

  • Mathematica
    Block[{d = 15, q, a, s}, a = Table[q = n-1; s = IntegerString[n]; Table[While[StringFreeQ[IntegerString[++q], s]]; q, d-n], {n, 0, d-1}]; Table[a[[n+1, k-n]], {k, d}, {n, 0, k-1}]] (* Paolo Xausa, Mar 01 2024 *)
  • PARI
    has(n,p,m=10^#Str(p))=until(p+!p>n\=10,n%m==p&&return(1))
Mat(vectorv(12,n,a=[];for(k=n--,oo,has(k,n)||next;a=concat(a,k);#a>12&&break);a))
for(i=1,11,for(j=1,i,print1(%[j,i-j+1]","))) \\ Read by antidiagonals

A293871 Numbers having 11 as substring of their digits.

Original entry on oeis.org

11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 211, 311, 411, 511, 611, 711, 811, 911, 1011, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Links

Crossrefs

Row 11 of A292690 and A293869.
Cf. A292451, A292731 (both partially coincide with this sequence, but no inclusion relation holds).
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: analog for substrings '0' through '9'.
Cf. A293870, A293872, A293873, A293874, A293875, A293876, A293877, A293878, A293879, A293880: same for substrings '10' - '20'.
Cf. A121031: subsequence of terms divisible by 11.
Numbers divisible by k and having k as a substring: A121022 (2), A121023 (3), A121024 (4), A121025 (5), A121026 (6), A121027 (7), A121028 (8), A121029 (9), A121030 (10), A121031 (11), A121032 (12), A121033 (13), A121034 (14), A121035 (15), A121036 (16), A121037 (17), A121038 (18), A121039 (19), A121040 (20).
Cf. A121041.

Programs

  • Mathematica
    Select[Range[2000], StringContainsQ[IntegerString[#], "11"] &] (* Paolo Xausa, Feb 25 2024 *)
  • PARI
    is_A293871 = has(n,p=11,m=10^#Str(p))=until(p>n\=10,n%m==p&&return(1))

Formula

a(n) ~ n. - Charles R Greathouse IV, Nov 02 2022

A293872 Numbers having '12' as a substring of their digits.

Original entry on oeis.org

12, 112, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 212, 312, 412, 512, 612, 712, 812, 912, 1012, 1112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 12 of A292690 and A293869. A121032 is the subsequence of multiples of 12.

Links

Crossrefs

Cf. A292690, A293869.
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: analog for '0' - '9'.
Cf. A293870, A293871, A293873, A293874, A293875, A293876, A293877, A293878, A293879, A293880: same for '10' - '20'.
Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040: subsequences of the above, containing only multiples of the pattern p.

Programs

  • Maple
    f:= proc(d) local i,x,y;
  sort(convert({seq(seq(seq(x+10^i*12+10^(i+2)*y, y=10^(d-3-i)..10^(d-2-i)-1),x=0..10^i-1),i=0..d-3),
seq(12*10^(d-2)+x,x=0..10^(d-2)-1)},list))
end proc:
seq(op(f(d)),d=2..4); # Robert Israel, Nov 20 2017
  • Mathematica
    Select[Range@ 1220, SequenceCount[IntegerDigits[#], {1, 2}] > 0 &] (* Michael De Vlieger, Nov 20 2017 *)
  • PARI
    is_A293872 = has(n, p=12, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

a(n) ~ n. - Charles R Greathouse IV, Nov 02 2022

A293877 Numbers having '17' as substring of their digits / decimal expansion.

Original entry on oeis.org

17, 117, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 217, 317, 417, 517, 617, 717, 817, 917, 1017, 1117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1217, 1317, 1417, 1517, 1617, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 1710, 1711, 1712, 1713
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 17 of A292690 and A293869. A121037 lists the terms which are divisible by 17.

Links

Crossrefs

Cf. A292690, A293869.
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: analog for '0' - '9'.
Cf. A293870, A293871, A293872, A293873, A293874, A293875, A293876, A293878, A293879, A293880: same for '10' - '20'.
Cf. A121041, A121022, A121023, A121024, A121025, A121026, A121027, A121028, A121029, A121030, A121031, A121032, A121033, A121034, A121035, A121036, A121037, A121038, A121039, A121040: subsequences of the above, containing only multiples of the pattern p.

Programs

  • Mathematica
    Select[Range[2000], StringContainsQ[IntegerString[#], "17"] &] (* Paolo Xausa, Feb 25 2024 *)
  • PARI
    is_A293877 = has(n, p=17, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

a(n) ~ n. - Charles R Greathouse IV, Nov 02 2022
Showing 1-10 of 29 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.