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.

Previous Showing 31-36 of 36 results.

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

A293873 Numbers having '13' as substring of their digits.

Original entry on oeis.org

13, 113, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 213, 313, 413, 513, 613, 713, 813, 913, 1013, 1113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1213, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 1310, 1311, 1312, 1313, 1314, 1315
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 13 of A292690 and A293869. A121033 is the subsequence of multiples of 13.

Links

Crossrefs

Cf. A292690, A293869.
Cf. A011540, A011531, A011532, A011533, A011534, A011535, A011536, A011537, A011538, A011539: analog for '0' - '9'.
Cf. A293870, A293871, A293872, 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

  • Mathematica
    Select[Range[1350],SequenceCount[IntegerDigits[#],{1,3}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 31 2017 *)
  • PARI
    is_A293873 = has(n, p=13, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

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

A293880 Numbers having '20' as substring of their digits.

Original entry on oeis.org

20, 120, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 220, 320, 420, 520, 620, 720, 820, 920, 1020, 1120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1220, 1320, 1420, 1520, 1620, 1720, 1820, 1920, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010
Offset: 1

Views

Author

M. F. Hasler, Oct 18 2017

Keywords

Comments

Row 20 of A292690 and A293869. A121040 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, A293879: same for '10' - '19'.
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[2100],SequenceCount[IntegerDigits[#],{2,0}]>0&] (* Harvey P. Dale, Jul 25 2021 *)
  • PARI
    is_A293880 = has(n, p=20, m=10^#Str(p))=until(p>n\=10, n%m==p&&return(1))

Formula

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

A239058 Numbers whose divisors all appear as a substring in their decimal expansion.

Original entry on oeis.org

1, 11, 13, 17, 19, 31, 41, 61, 71, 101, 103, 107, 109, 113, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 241, 251, 271, 281, 311, 313, 317, 331, 401, 419, 421, 431, 461, 491, 521, 541, 571, 601, 613, 617, 619, 631, 641, 661, 691, 701, 719, 751, 761, 811, 821, 881, 911, 919, 941, 971
Offset: 1

Views

Author

M. F. Hasler, Mar 09 2014

Keywords

Comments

A subsequence of A092911 (all divisors can be formed using the digits of the number) which is a subsequence of A011531 (numbers having the digit 1).
Are 1 and 125 the only nonprime terms in this sequence?
No: 17692313, 4482669527413081, 21465097175420089, and 567533481816008761 are members. - Charles R Greathouse IV, Mar 09 2014
See A239060 for the nonprime terms of this sequence, which include in particular the squares of terms of A115738 (unless such a square would not have a digit 1).

Examples

			All primes having the digit 1 (A208270) are in this sequence, because {1, p} are the only divisors of a prime p.
The divisors of 125 are {1, 5, 25, 125}; it can be seen that all of them occur as a substring in 125, therefore 125 is in this sequence.

Links

Crossrefs

Cf. A092911, A011531, A121041, A121022-A121040, A018834.

Programs

  • PARI
    is(n,d=vecextract(divisors(n),"^-1"))={ setminus(select(x->x<10,d),Set(digits(n)))&&return;!for(L=2,#Str(d[#d]),setminus(select(x->x
<10^L&&x>=10^(L-1),d),Set(concat(vector(L,o,digits(n\10^(L-o),10^L)))))&&return)}
  • PARI
    overlap(long,short)=my(D=10^#digits(short)); while(long>=short, if(long%D==short,return(1));long\=10); 0
is(n)=my(d=divisors(n)); forstep(i=#d-1,1,-1, if(!overlap(n,d[i]), return(0))); 1 \\ Charles R Greathouse IV, Mar 09 2014

A239060 Nonprime numbers whose divisors all appear as a substring in the number's decimal expansion.

Original entry on oeis.org

1, 125, 17692313
Offset: 1

Views

Author

M. F. Hasler, Mar 09 2014

Keywords

Comments

This is the subsequence of A239058 without the primes having a digit 1, A208270. It is thus a subsequence of A092911 (all divisors can be formed using the digits of the number) which is a subsequence of A011531 (numbers having the digit 1).
The term a(3)=17692313=A239058(870356), as well as the numbers 4482669527413081, 21465097175420089, and 567533481816008761 which are also members, were found by Charles R Greathouse IV, Mar 09 2014
The square of any term of A115738 is a member of this sequence. The above larger examples are of that form.
a(4) > 10^12. - Giovanni Resta, Sep 08 2018

Examples

			The divisors of 17692313 are {1, 23, 769231, 17692313}; it can be seen that all of them occur as a substring in 17692313, therefore 17692313 is in this sequence.

Links

Crossrefs

Cf. A092911, A011531, A121041, A121022-A121040, A018834.

Programs

  • PARI
    is(n)=!isprime(n)&&is_A239058(n)
  • PARI
    overlap(long,short)=my(D=10^#digits(short)); while(long>=short, if(long%D==short,return(1));long\=10); 0
is(n)=my(d=divisors(n)); #d!=2 && !forstep(i=#d-1,1,-1, if(!overlap(n,d[i]), return(0))) \\ Charles R Greathouse IV, Mar 09 2014

A044352 Numbers n such that string 2,0 occurs in the base 10 representation of n but not of n-1.

Original entry on oeis.org

20, 120, 200, 220, 320, 420, 520, 620, 720, 820, 920, 1020, 1120, 1200, 1220, 1320, 1420, 1520, 1620, 1720, 1820, 1920, 2000, 2120, 2200, 2220, 2320, 2420, 2520, 2620, 2720, 2820, 2920, 3020, 3120, 3200, 3220, 3320, 3420
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

This is a (thin) subsequence of the terms of A121040 ending with a 2 followed by one or more zeros and which do not otherwise contain a 2 followed by a 0. This also demonstrates that this sequence is a 10-automatic. - Charles R Greathouse IV, Apr 18 2020

Links

Crossrefs

Subsequence of A121040.

Programs

  • Mathematica
    SequencePosition[Table[If[SequenceCount[IntegerDigits[n],{2,0}]>0,1,0],{n,3500}],{0,1}][[All,2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 24 2018 *)
Previous Showing 31-36 of 36 results.

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

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