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 12 results. Next

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

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

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

A293870 Numbers having '10' as substring of their digits.

Original entry on oeis.org

10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 210, 310, 410, 510, 610, 710, 810, 910, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 10 of A292690 and A293869.

Links

Crossrefs

Cf. A292690, A293869.
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: analog for '0' - '9'.
Cf. A293871, A293872, A293873, A293874, A293875, A293876, A293877, A293878, A293879, A293880: same for '11' - '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[1100],SequenceCount[IntegerDigits[#],{1,0}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 07 2019 *)
  • PARI
    is_A293870 = has(n, p=10, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

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

A293874 Numbers having '14' as substring of their digits.

Original entry on oeis.org

14, 114, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 214, 314, 414, 514, 614, 714, 814, 914, 1014, 1114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1214, 1314, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 1410, 1411, 1412, 1413, 1414, 1415, 1416
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 14 of A292690 and A293869.

Links

Crossrefs

Cf. A292690, A293869. A121034 lists the terms which are divisible by 14.
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: analog for '0' - '9'.
Cf. A293870, A293871, A293872, A293873, 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

  • Mathematica
    Select[Range[2000], StringContainsQ[IntegerString[#], "14"] &] (* Paolo Xausa, Feb 25 2024 *)
  • PARI
    is_A293874 = has(n, p=14, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

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

A293875 Numbers having '15' as substring of their digits.

Original entry on oeis.org

15, 115, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 215, 315, 415, 515, 615, 715, 815, 915, 1015, 1115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1215, 1315, 1415, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 1510, 1511, 1512, 1513, 1514, 1515
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 15 of A292690 and A293869. A121035 lists the terms which are divisible by 15.

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, 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

  • Mathematica
    Select[Range[2000], StringContainsQ[IntegerString[#], "15"] &] (* Paolo Xausa, Feb 25 2024 *)
  • PARI
    is_A293875 = has(n, p=15, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

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

A293876 Numbers having '16' as substring of their digits / decimal expansion.

Original entry on oeis.org

16, 116, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 216, 316, 416, 516, 616, 716, 816, 916, 1016, 1116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1216, 1316, 1416, 1516, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 1610, 1611, 1612, 1613, 1614
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 16 of A292690 and A293869. A121036 lists the terms which are divisible by 16.

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, 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

  • Mathematica
    Select[Range[2000], StringContainsQ[IntegerString[#], "16"] &] (* Paolo Xausa, Feb 25 2024 *)
  • PARI
    is_A293876 = has(n, p=16, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

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

A293878 Numbers having '18' as substring of their digits / decimal expansion.

Original entry on oeis.org

18, 118, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 218, 318, 418, 518, 618, 718, 818, 918, 1018, 1118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1218, 1318, 1418, 1518, 1618, 1718, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1812
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 16 of A292690 and A293869. A121038 lists the terms which are divisible by 18.

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, A293877, 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[#], "18"] &] (* Paolo Xausa, Feb 25 2024 *)
  • PARI
    is_A293878 = has(n, p=18, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

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

A293879 Numbers having '19' as substring of their digits.

Original entry on oeis.org

19, 119, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 219, 319, 419, 519, 619, 719, 819, 919, 1019, 1119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1219, 1319, 1419, 1519, 1619, 1719, 1819, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 1910, 1911
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 19 of A292690 and A293869. A121039 lists the terms which are divisible by 19.

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, A293877, A293878, 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],SequenceCount[IntegerDigits[#],{1,9}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 11 2019 *)
  • PARI
    is_A293879 = has(n, p=19, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

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