A039938 -id:A039938 - cp's OEIS frontend

A285846 A039938 with duplicates removed.

7, 37, 237, 1789, 4357, 14379, 19587, 93957, 189572, 189597, 1234397, 1839597, 1958798, 1983957, 3978594, 11983957, 19596487, 29195397, 39599197, 195991487, 339799143, 395991697, 1429199397, 1679895983, 1983994799, 2239951987, 11959939917, 15991995897

Offset: 1

J. Lowell, Apr 27 2017

Any proof that this sequence is infinite?

This sequence is infinite because A039938 is indeed infinite and for any number k there is a multiple of k which does not contain a '7', so A039938 contains infinitely many distinct terms. Both parts are easy to prove. - Giovanni Resta, Feb 26 2019

Giovanni Resta, Table of n, a(n) for n = 1..32

Cf. A039938.

Subsequence of A011537.

Union@ 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 *)

a(19)-a(28) from Giovanni Resta, Apr 27 2017

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

Erich Friedman

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
51
531
2571
15703
90271
102053
530102
4550102
4570102
4580102
22900501
134003006
1002003005
5001002003
5003001002
30005001002
30005002001
200030005001
1000200030005

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

Giovanni Resta, Table of n, a(n) for n = 1..2443

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

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

Erich Friedman

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

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

Giovanni Resta, Table of n, a(n) for n = 1..287

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

More terms from Patrick De Geest, Oct 15 1999

A039934 Smallest k for which k, 2k, ..., nk 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

Erich Friedman

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

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

Giovanni Resta, Table of n, a(n) for n = 1..168

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

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

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

Erich Friedman

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

Giovanni Resta, Table of n, a(n) for n = 1..2047

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

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

More terms from Patrick De Geest, Oct 15 1999

A039936 Smallest k for which k, 2k, ... nk all contain the digit 5.

Original entry on oeis.org

5, 25, 25, 125, 125, 125, 125, 625, 625, 625, 625, 625, 625, 625, 625, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 3125, 15625, 15625, 15625, 15625, 15625, 15625, 15625, 15625, 15625, 15625, 15625

Offset: 1

Erich Friedman

			a(3)=25 since 25, 50, and 75 all contain a 5.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A039932, A039933, A039934, A039935, A039937, A039938, A039939, A039940.

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

Erich Friedman

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

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

Giovanni Resta, Table of n, a(n) for n = 1..196

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

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

Erich Friedman

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

Giovanni Resta, Table of n, a(n) for n = 1..262

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

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

Erich Friedman

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

Giovanni Resta, Table of n, a(n) for n = 1..10000

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

More terms from Patrick De Geest, Oct 15 1999

A285454 Least number x such that x^n has n digits equal to k. Case k = 7.

Original entry on oeis.org

7, 76, 83, 118, 206, 959, 1083, 726, 1387, 1114, 3313, 4011, 2184, 3881, 4792, 13071, 11564, 15523, 9208, 15232, 17771, 46336, 33815, 39147, 18083, 27624, 63435, 77276, 24354, 92341, 15776, 67006, 112877, 54468, 67996, 109996, 99376, 154083, 58937, 148722, 77335

Offset: 1

Paolo P. Lava, Apr 19 2017

			a(4) = 118 because 118^4 = 193877776 has 4 digits '7' and is the least number to have this property.

Martin Gossow, Table of n, a(n) for n = 1..100

Cf. A039938.

P:=proc(q,h) local a,j,k,n,t; for n from 1 to q do for k from 1 to q do
a:=convert(k^n,base,10); t:=0; for j from 1 to nops(a) do if a[j]=h then t:=t+1; fi; od;
if t=n then print(k); break; fi; od; od; end: P(10^9,7);

f[n_] := Block[{k = 1}, While[ Count[ IntegerDigits[k^n], 7] != n, k++]; k]; Array[f, 41] (* Robert G. Wilson v, Apr 30 2017 *)

cp's OEIS Frontend

A285846 A039938 with duplicates removed.

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

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

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

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

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A039936 Smallest k for which k, 2k, ... nk all contain the digit 5.

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

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

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

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