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 41-47 of 47 results.

A342308 Numbers whose fifth powers are zeroless pandigital.

Original entry on oeis.org

193, 353, 398, 678, 695, 697, 744, 768, 776, 793, 868, 883, 966, 968, 983, 1045, 1075, 1079, 1089, 1097, 1098, 1114, 1129, 1148, 1186, 1193, 1212, 1291, 1311, 1403, 1405, 1442, 1544, 1576, 1584, 1643, 1715, 1734, 1746, 1775, 1795, 1853, 1868, 1888, 1917, 1944, 1953, 1971, 1974, 1996
Offset: 1

Views

Author

Tanya Khovanova, Mar 08 2021

Keywords

Comments

Numbers n such that A000584(n) is in { A050289 }.

Examples

			193^5 = 267785184193, and contains all the digits 1 through 9.

Links

Crossrefs

Cf. A000584, A050289.

Programs

  • Maple
    q:= n-> is({convert(n^5, base, 10)[]}={$1..9}):
select(q, [$1..2000])[];  # Alois P. Heinz, Mar 08 2021
  • Mathematica
    Select[Range[2000],
Sort[ Union[IntegerDigits[#^5]]] == {1, 2, 3, 4, 5, 6, 7, 8, 9} &]
  • PARI
    isok(m) = my(d=digits(m^5)); vecmin(d) && (#Set(d) == 9); \\ Michel Marcus, Mar 09 2021
  • Python
    A342308_list = [n for n in range(1,10**5) if set(str(n**5)) == {'1', '2', '3', '4', '5', '6', '7', '8', '9'}] # Chai Wah Wu, Mar 08 2021

A039667 Numbers k that together with their double and triple contain every digit from 1-9 exactly once.

Original entry on oeis.org

192, 219, 273, 327
Offset: 0

Views

Author

Felice Russo

Keywords

Examples

			k=327 -> 2k=654 -> 3k=981 and 327654981 is a 'nine-digit' number.

References

  • D. Wells, Curious and interesting numbers, Penguin Books, p. 128.

Links

Crossrefs

Cf. A050289.

Programs

  • Mathematica
    pdnQ[n_]:=Sort[Flatten[IntegerDigits[{n,2n,3n}]]]==Range[9]; Select[Range[987],pdnQ] (* Harvey P. Dale, Jul 07 2012 *)

Extensions

Corrected by Patrick De Geest, Mar 15 2000
Better definition from Tanya Khovanova, Mar 08 2021

A175547 Lexicographically earliest sequence of increasing 9-digit zeroless anagrams that share no common digit place with previous terms.

Original entry on oeis.org

123456789, 214365897, 341278956, 432189675, 567891234, 658917342, 789523461, 896742513, 975634128
Offset: 1

Views

Author

Zak Seidov, Jun 24 2010

Keywords

Crossrefs

Cf. A114288 / A112454 Lexicographically earliest / maximal solution of any 9 X 9 sudoku. A050289 Zeroless pandigital numbers: numbers containing the digits 1-9 and no 0's.

A288941 a(n) is the least natural number not included earlier having all decimal digits except the digits in n; if n is pandigital or zeroless pandigital, a(n) is simply the least natural number not included earlier.

Original entry on oeis.org

123456789, 203456789, 103456789, 102456789, 102356789, 102346789, 102345789, 102345689, 102345679, 102345678, 23456789, 203456798, 30456789, 20456789, 20356789, 20346789, 20345789, 20345689, 20345679, 20345678, 13456789
Offset: 0

Views

Author

Rick L. Shepherd, Jun 19 2017

Keywords

Comments

A rearrangement of the natural numbers by definition as there are an infinite number of pandigital numbers (A171102) and zeroless pandigital numbers (A050289).
Leading zeros are not permitted. The "zeroless pandigital" criterion is used also because there is just one number with the digit 0 only and we wish all terms to be distinct.
What values are a(A050289(1)) = a(123456789) and a(A171102(1)) = a(1023456789)?

Examples

			For n = 0, a(0) = 123456789, the least natural number containing all decimal digits but the digit 0.
For n = 11, a(11) = 203456798, which has all decimal digits but the digit 1 and is the first such number with that property that is larger than 203456789 (= a(1)).

Links

Crossrefs

Cf. A050289, A171102.

A339498 Number of zeroless strictly pandigital numbers divisible by the n-th prime.

Original entry on oeis.org

161280, 362880, 40320, 51752, 31680, 27776, 21271, 19138, 15788, 12613, 11707, 9072, 8832, 8423, 7725, 6822, 6241, 5937, 5454, 5113, 4796, 4629, 4310, 4122, 3744, 3168, 3528, 3410, 3305, 3160, 2826, 2827, 2778, 2619, 2316, 2297, 2297, 2173, 2163, 2094, 2077, 2027, 1879, 1915, 1836, 1780, 1773
Offset: 1

Views

Author

G. L. Honaker, Jr., Dec 07 2020

Keywords

Comments

Calculated by Chuck Gaydos.
a(4620), for prime(4620) = 44449, is the first zero entry. The last nonzero entry is a(6289143) for prime 109739359 = 987654231 / 9. - Michael S. Branicky, Dec 07 2020

Crossrefs

Cf. A000040, A050289.

Programs

  • Python
    from sympy import prime
from itertools import permutations
def zeroless_pans():
    for p in permutations("123456789"):
        yield int("".join(p))
def a(n):
    pn = prime(n)
    return sum(zlp%pn==0 for zlp in zeroless_pans())
print([a(n) for n in range(1, 43)]) # Michael S. Branicky, Dec 07 2020

A354708 a(n) is the number of 9-digit zeroless pandigital numbers that are divisible by 3^n.

Original entry on oeis.org

362880, 362880, 362880, 122472, 40824, 13590, 4526, 1490, 520, 172, 58, 22, 6, 2, 0
Offset: 0

Views

Author

Fletcher Thompson, Jun 03 2022

Keywords

Comments

The sequence ends at a(14) because no 9-digit zeroless pandigital number is divisible by 3^14. The two numbers divisible by 3^13 are 618597324 and 647295138.

Crossrefs

Cf. A050289.

A358705 Zeroless pandigital numbers whose square has each digit 1 to 9 twice.

Original entry on oeis.org

345918672, 351987624, 359841267, 394675182, 429715863, 439516278, 487256193, 527394816, 527498163, 528714396, 572493816, 592681437, 729564183, 746318529, 749258163, 754932681, 759142683, 759823641, 762491835, 783942561, 784196235, 845691372, 891357624, 914863275, 915786423, 923165487, 928163754, 976825431
Offset: 1

Views

Author

Zhining Yang, Nov 27 2022

Keywords

Examples

			345918672 is a term since its square 119659727638243584 contains all digits 1..9 twice each.

Crossrefs

Cf. A050289, A199630.

Programs

  • Maple
    R:= NULL:
for t in combinat:-permute([$1..9]) do
  x:= add(t[i]*10^(i-1),i=1..9);
  if sort(convert(x^2,base,10)) = [seq(i$2,i=1..9)] then
    R:= R, x
  fi
od:
sort([R]); # Robert Israel, Nov 27 2022
  • Python
    from itertools import permutations as per
a=[]
for n in [int(''.join(d)) for d in per('123456789', 9)]:
    if all(str(n**2).count(d) ==2 for d in '123456789'):
        a.append(n)
print(a)
Previous Showing 41-47 of 47 results.

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