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 1-8 of 8 results.

A039938 Smallest k for which k, 2k, ... nk all contain the digit 7.

Original entry on oeis.org

7, 37, 237, 1789, 4357, 14379, 19587, 93957, 189572, 189572, 189597, 189597, 189597, 1234397, 1839597, 1958798, 1983957, 1983957, 1983957, 1983957, 1983957, 1983957, 3978594, 11983957, 19596487, 29195397, 29195397, 29195397
Offset: 1

Views

Author

Erich Friedman

Keywords

Examples

			a(2)=37 since 37 and 74 contain a 7.

Links

Crossrefs

Cf. A039932, A039933, A039934, A039935, A039936, A039937, A039939, A039940.

Programs

  • Mathematica
    Table[SelectFirst[Range[10^6], Times @@ Boole@ Map[DigitCount[#, 10, 7] > 0 &, # Range@ n] > 0 &], {n, 12}] (* Michael De Vlieger, Apr 27 2017, Version 10 *)

Extensions

More terms from Patrick De Geest, Oct 15 1999

A039932 Smallest number k for which k, 2k, ... nk all contain the digit 1.

Original entry on oeis.org

1, 51, 51, 531, 2571, 2571, 2571, 15703, 15703, 15703, 15703, 15703, 15703, 15703, 90271, 90271, 90271, 90271, 90271, 90271, 90271, 90271, 102053, 530102, 530102, 530102, 530102, 530102, 530102, 530102, 530102, 530102, 530102, 530102, 530102
Offset: 1

Views

Author

Erich Friedman

Keywords

Comments

There are relatively few distinct terms in this sequence. The following list shows the frequencies of a(n) for n=1..2443. - Georg Fischer, Feb 21 2021
1 1
2 51
1 531
3 2571
7 15703
8 90271
1 102053
15 530102
5 4550102
1 4570102
4 4580102
49 22900501
53 134003006
93 1002003005
200 5001002003
1 5003001002
223 30005001002
1 30005002001
576 200030005001
1199 1000200030005

Examples

			a(3)=51 since 51, 102, and 153 all contain a 1.

Links

Crossrefs

Cf. A039933, A039934, A039935, A039936, A039937, A039938, A039939, A039940.

Extensions

More terms from Patrick De Geest, Oct 15 1999

A039933 Smallest k for which k, 2k, ... n*k all contain the digit 2.

Original entry on oeis.org

2, 12, 124, 624, 624, 642, 4062, 4062, 4128, 4128, 23041, 23041, 23041, 23041, 144032, 144032, 144032, 144032, 144032, 144032, 144032, 1201804, 1201804, 1201804, 1276048, 1276048, 1276048, 1276048, 1276048, 1276048, 8020604
Offset: 1

Views

Author

Erich Friedman

Keywords

Comments

a(288) > 5*10^11. - Giovanni Resta, Apr 27 2017

Examples

			a(3)=624 since 624, 1248, and 1872 all contain a 2.

Links

Crossrefs

Cf. A039932, A039934, A039935, A039936, A039937, A039938, A039939, A039940.

Extensions

More terms from Patrick De Geest, Oct 15 1999

A039934 Smallest k for which k, 2*k, ..., n*k all contain the digit 3.

Original entry on oeis.org

3, 153, 1153, 1183, 3465, 7673, 7673, 7673, 65913, 65913, 65913, 76923, 232767, 232767, 232767, 232767, 232767, 2307767, 2307767, 2307767, 2307767, 3076923, 6923313, 17078903, 19507893, 56695913, 56695913, 113322666, 113322666
Offset: 1

Views

Author

Erich Friedman

Keywords

Comments

a(169) > 7*10^11. - Giovanni Resta, Apr 27 2017
a(169) = a(170) = ... = a(188) = 1538461526061, and a(189) > 2*10^12. - David Radcliffe, Sep 12 2018

Examples

			a(2)=153 since 153 and 306 both contain a 3, and 153 is the smallest number for which this is the case.

Links

Crossrefs

Cf. A039932, A039933, A039935, A039936, A039937, A039938, A039939, A039940.

Programs

  • Python
    from itertools import count, islice
def agen(startn=1, startk=1):
    n = startn
    for k in count(startk):
        ki, nn = k, 0
        while "3" in str(ki): ki += k; nn += 1
        while n < ki//k: yield k; n += 1
print(list(islice(agen(), 22))) # Michael S. Branicky, Jul 31 2022

Extensions

More terms from Patrick De Geest, Oct 15 1999

A039935 Smallest k for which k, 2k, ... nk all contain the digit 4.

Original entry on oeis.org

4, 24, 47, 471, 487, 1248, 1249, 6248, 6249, 6249, 12493, 12493, 12493, 12493, 12498, 31249, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 62499, 312497, 312497, 312497, 624984, 624984, 624984, 624984, 624984
Offset: 1

Views

Author

Erich Friedman

Keywords

Examples

			a(3) = 47 since 47, 94 and 141 all contain a 4.

Links

Crossrefs

Cf. A039932, A039933, A039934, A039936, A039937, A039938, A039939, A039940.

Programs

  • Python
    def aupton(terms):
  k, n, alst = 1, 1, []
  while len(alst) < terms:
    while not all(str(i*k).count('4') > 0 for i in range(1, n+1)): k += 1
    while str(n*k).count('4') > 0: alst.append(k); n += 1
    k += 1
  return alst[:terms]
print(aupton(39)) # Michael S. Branicky, Apr 24 2021

Extensions

More terms from Patrick De Geest, Oct 15 1999

A039937 Smallest k for which k, 2k, ... nk all contain the digit 6.

Original entry on oeis.org

6, 63, 563, 1563, 1632, 3216, 12316, 23266, 66321, 66321, 76923, 76923, 156328, 280692, 566331, 566331, 566331, 2307692, 2307692, 2307692, 2307692, 2307692, 2307692, 2307692, 2307692, 11533664, 23306676, 23306676, 23306676, 23306676
Offset: 1

Views

Author

Erich Friedman

Keywords

Comments

a(197) > 10^12. - Giovanni Resta, Apr 27 2017

Examples

			a(2)=63 since 63 and 126 contain a 6.

Links

Crossrefs

Cf. A039932, A039933, A039934, A039935, A039936, A039938, A039939, A039940.

Extensions

More terms from Patrick De Geest, Oct 15 1999

A039939 Smallest k for which k, 2k, ... nk all contain the digit 8.

Original entry on oeis.org

8, 84, 284, 2842, 8937, 8964, 8964, 85964, 89641, 89641, 89641, 89729, 296984, 429817, 897299, 897299, 897299, 897299, 897299, 897299, 897299, 897299, 897299, 8697299, 9897947, 9929817, 9929817, 9929817, 9929817, 9929817, 9929817
Offset: 1

Views

Author

Erich Friedman

Keywords

Examples

			a(2)=84 since 84 and 168 contain a 8.

Links

Crossrefs

Cf. A039932, A039933, A039934, A039935, A039936, A039937, A039938, A039940.

Extensions

More terms from Patrick De Geest, Oct 15 1999

A039940 Smallest k for which k, 2k, ... nk all contain the digit 9.

Original entry on oeis.org

9, 49, 97, 98, 98, 99, 99, 99, 99, 99, 99, 499, 992, 993, 993, 994, 994, 994, 995, 995, 995, 995, 996, 996, 996, 996, 996, 997, 997, 997, 997, 997, 997, 997, 997, 997, 997, 998, 998, 998, 998, 998, 998, 998, 998, 998, 998, 998, 998, 998, 998, 998, 998, 998
Offset: 1

Views

Author

Erich Friedman

Keywords

Examples

			a(11)=99 since 99, 198, 297, 396, 495, 594, 693, 792, 891, 990, and 1089 all contain a 9.

Links

Crossrefs

Cf. A039932, A039933, A039934, A039935, A039936, A039937, A039938, A039939.

Extensions

More terms from Patrick De Geest, Oct 15 1999
Showing 1-8 of 8 results.

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